tag:blogger.com,1999:blog-58088561672987060532023-11-16T02:35:33.334-08:00School electronicSchool electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comBlogger40125tag:blogger.com,1999:blog-5808856167298706053.post-3017323277694578502023-02-28T13:02:00.000-08:002023-02-28T13:02:53.382-08:00History and evolution of electronics<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRUXvxTrrLkUuNz22_R781ZopXwraFzfMJpua57MbBf7DBEwyV7-MJS7a3dM9lR87ICcvfP-erSS-3iIQgXHQdWUZG0GuLBlAvYXWaaVKxKZX5YbHwi1gjxKlMER3hg0jnBQDXcn3faODx3l0UErLRVTFgWYm_uAHV8TX6aTyvJQgbFax5gaiQshxn/s1024/history-evolution-of-electronics.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="History and evolution of electronics" border="0" data-original-height="512" data-original-width="1024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRUXvxTrrLkUuNz22_R781ZopXwraFzfMJpua57MbBf7DBEwyV7-MJS7a3dM9lR87ICcvfP-erSS-3iIQgXHQdWUZG0GuLBlAvYXWaaVKxKZX5YbHwi1gjxKlMER3hg0jnBQDXcn3faODx3l0UErLRVTFgWYm_uAHV8TX6aTyvJQgbFax5gaiQshxn/w640-h320/history-evolution-of-electronics.jpg" title="History and evolution of electronics" width="640" /></a></div><br /><p><br /></p><p><head>
<meta content="The major milestones in the evolution of present day electronics and the contributions of great scientists" name="description"></meta>
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</div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiTTq2m86MblXc5TBhTOFgJawaLJIHPoYy9eJjM4VOPQEjW9GYEHpUatC6PNX77wRp4ocrrra8JBE6-42cYdjaf29DbM2RlFDcgzsXus8RppzlpgaU_Tczhr0KsaehQ8Zh2CzGeziG2SU/s1600/histro+of+electronics.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="38" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiTTq2m86MblXc5TBhTOFgJawaLJIHPoYy9eJjM4VOPQEjW9GYEHpUatC6PNX77wRp4ocrrra8JBE6-42cYdjaf29DbM2RlFDcgzsXus8RppzlpgaU_Tczhr0KsaehQ8Zh2CzGeziG2SU/s320/histro+of+electronics.png" width="320" /></a></div>
<ol><li>In 1791 <b>Luigi Galvani</b>: Professor of anatomy (university
of bologna) with the help of series of experiments showed the presence
of electricity in animals (specifically frogs).</li><li>In 1799 <b>Charles coulomb</b>: One famous scientist of the 18th
century demonstrated that there existed a force between any two
charges, this force could be either attractive force or repulsive force
and this force is also influenced by the distance of separation
between the two charges.</li><li>In 1799 <b>Allessandro Volta</b> : An Italian scientist credited
with the invention of battery. He was the first to develop a battery
know as the voltaic cell that could produce electricity as a result of
chemical reaction.</li><li>In 1820, Hans <b>Christian oersted</b> showed that a magnetic
field is associated whenever current flows through a conductor. To
demonstrate this effect he connect a copper wire to the terminals of a
battery and a switch and placed a magnetic compass near the wire. When
the switch was close current started flowing in the wire and a
deflection was seen in the compass indicating that current carrying
conductor has an associated magnetic field.</li><li>In 1827 <b>George simon</b> <b>Ohm,</b> a germen physicist derived
the relation between the voltage applied (V), the current (I), and the
resistance of a circuit. This is the famous and the most basic law
Ohm’s law. It is given as <b>V=IR</b>.</li><li>In 1831 <b>Michael Faraday</b> , a British scientist after the
discovery by Oersted that a magnetic field is associated with the
conductor carrying current, Faraday through a series of experiments
discovered that the vice versa is possible i.e. current can be
generated by using time varying magnetic field. This phenomenon was
termed as the Electromagnetic induction which is the basic underlying
principle of the working of generators.</li><li>In 1864 <b>James Clerk Maxwell</b>, A British Physicist developed
the electromagnetic field equations that today is referred to as
Maxwell’s equations. He also formulated an important theory known as the
electromagnetic theory of light, which told that electromagnetic waves
travel in free space at the speed of light.</li><li>In 1888 <b>Heinrich Hertz</b>, Based on the predictions of
Maxwell’s electromagnetic theory wanted to experimentally verify the
theory. He performed various experiments according to what Maxwell’s
theory and successfully demonstrated to the world the effect of
electromagnetic radiation through space .</li><li>In 1895 <b>Guglielmo Marconi</b> put together the predictions of
Maxwell and the experiments of Hertz to send electromagnetic signals
through space and was successful in setting up the first transatlantic
wireless communication system.</li><li>In 1948, <b>William Schockley</b>, <b>John Bardeen</b> and <b>Watter Brattain</b> developed the transistor.</li><li><b>Nikola Tesla</b>: One great scientist without whom our today’s
world would have been dark. Yes he invented alternating current
(Popularly known as <b>AC</b>) and gave light to the world. He also has his name <b>Tesla</b> as the unit of magnetic field added to his credit. </li></ol>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-83738507099321308122023-02-28T12:58:00.001-08:002023-02-28T12:58:52.438-08:00Convert hexadecimal to decimal number<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZb_-BF3tV5vMMFUg9okXCePRBJ_p6r3dJUTqrMEKlkDZIJb5T5s-PtVxfZxym61ePNfZ9ZKw737EJLVVzgp4Zkb8kgo-1hwCgCBcPjz2JkqK6Vg8NfMychcJSfTIRa-GMv9L4q6HHgsyZrnNxE6YMU2DYxZ7JSwGtW9NOo64TnWh1l6ZW8bxPufeO/s1024/hexadecimal-to-decimal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Convert hexadecimal to decimal number" border="0" data-original-height="512" data-original-width="1024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZb_-BF3tV5vMMFUg9okXCePRBJ_p6r3dJUTqrMEKlkDZIJb5T5s-PtVxfZxym61ePNfZ9ZKw737EJLVVzgp4Zkb8kgo-1hwCgCBcPjz2JkqK6Vg8NfMychcJSfTIRa-GMv9L4q6HHgsyZrnNxE6YMU2DYxZ7JSwGtW9NOo64TnWh1l6ZW8bxPufeO/w640-h320/hexadecimal-to-decimal.jpg" title="Convert hexadecimal to decimal number" width="640" /></a></div><br /><p><br /></p><div dir="ltr" style="text-align: left;" trbidi="on"><div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><div class="lwptoc_i" style="background: rgb(255, 255, 255); border: 1px solid rgb(173, 173, 173); box-sizing: inherit; color: #333333; display: inline-block; padding: 14px 18px 18px; text-align: left;"><div class="lwptoc_header" style="box-sizing: inherit; margin-bottom: 6px;"><b class="lwptoc_title" style="box-sizing: inherit; font-weight: 700;">Contents</b><span> </span><br /></div><div class="lwptoc_items lwptoc_items-visible" style="box-sizing: inherit; font-size: 15.3px;"><div class="lwptoc_itemWrap" style="box-sizing: inherit;"><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/2012/01/convert-hexadecimal-to-decimal-number.html#How-to-Convert-Hex-to-Decimal" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">How to Convert Hexadecimal to Decimal</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/2012/01/convert-hexadecimal-to-decimal-number.html#Hex-to-Decimal-Examples" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Hexadecimal to Decimal Examples</span></a><div class="lwptoc_itemWrap" style="box-sizing: inherit; margin: 2px 0px 0px 14px;"><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 0px;"><a href="https://www.schoolelectronic.com/2012/01/convert-hexadecimal-to-decimal-number.html#Example-1-Convert-2-5-A-16-Hexadecimal-to-Decimal-10" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Example 1: Convert ( 2 5 A )16 Hexadecimal to Decimal ( ? )10</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#Example-2-Convert-2-0-D-0-16-Hex-to-decimal-10" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Example 2: Convert ( 2 0 D 0 )16 Hex to decimal ( ? )10</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#Example-3-Convert-F-F-F-F-16-10" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Example 3 : Convert ( F F F F )16= ( ? )10</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#Example-4-Convert-A-B-C-0-16-10" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Example 4 : Convert ( A B C 0 )16= ( ? )10</span></a></div></div></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#Hex-to-Decimal-Chart" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Hex to Decimal Chart</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#Hex-to-Decimal-FAQs" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Hex to Decimal FAQs</span></a><div class="lwptoc_itemWrap" style="box-sizing: inherit; margin: 2px 0px 0px 14px;"><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 0px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#What-is-20-hex-to-decimal" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">What is 20 hex to decimal?</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#What-is-3f-hex-to-decimal" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">What is 3f hex to decimal?</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/hexadecimal-to-decimal/#What-is-abc-hexadecimal-to-decimal" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">What is abc hexadecimal to decimal?</span></a></div></div></div></div></div></div></div><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">We
can convert hexadecimal to decimal by simply representing the given
each digit of the given Hexadecimal number as sum of powers of 16, since
for hexadecimal number system 16 is the base or radix. Here we first
convert each individual hexadecimal digit separately and then add it
together to get the final decimal equivalent. Detailed steps explaining
the process of converting Hexadecimal to decimal, with illustrated
examples of<span> </span><a class="rank-math-link" href="https://www.schoolelectronic.com/number-systems/" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">hexadecimal<span> </span></a>to decimal conversions.</p> <h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="How-to-Convert-Hex-to-Decimal" style="box-sizing: inherit;">How to Convert Hexadecimal to Decimal</span></h2><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;"><span style="box-sizing: inherit; text-decoration: underline;">Step 1:</span></b><span> </span>First
we write down the given hexadecimal number separately and identify the
LSD and MSD for hexadecimal numbers with only integer part and no
fractional part.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;"><span style="box-sizing: inherit; text-decoration: underline;">Step 2:</span></b><span> </span>We then represent each digit of the given hexadecimal number as powers of 16, starting from 16<sup style="bottom: 1ex; box-sizing: inherit; font-size: 12.75px; height: 0px; line-height: 0; position: relative; vertical-align: baseline;">0</sup><span> </span>from right to left.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;"><span style="box-sizing: inherit; text-decoration: underline;">Step 3:</span></b><span> </span>We then evaluate the power of 16 values such as 16<sup style="bottom: 1ex; box-sizing: inherit; font-size: 12.75px; height: 0px; line-height: 0; position: relative; vertical-align: baseline;">0</sup><span> </span>is 1 and 16<sup style="bottom: 1ex; box-sizing: inherit; font-size: 12.75px; height: 0px; line-height: 0; position: relative; vertical-align: baseline;">1</sup><span> </span>is 16. And from the<span> </span><a class="rank-math-link" href="https://www.schoolelectronic.com/number-system-conversion/#decimal-binary-octal-hexadecimal-number-system-conversion-table" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">number system conversion table</a><span> </span>we
can identify the decimal equivalent of individual hexadecimal digits
such as for example the decimal equivalent of hexadecimal digit A is 10.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;"><span style="box-sizing: inherit; text-decoration: underline;">Step 4:</span></b><span> </span>We
then multiply the decimal equivalent obtained from the number system
table with the evaluated power of 16 values, and write it down as sum of
products.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;"><span style="box-sizing: inherit; text-decoration: underline;">Step 5:</span></b><span> </span>We then add all the individual products and this sum total gives the final decimal equivalent of the given hexadecimal number.</p></div><div dir="ltr" style="text-align: left;" trbidi="on"> </div><div dir="ltr" style="text-align: left;" trbidi="on">The following show illustrated examples of hexadecimal to decimal converstions<br />
<div dir="ltr" trbidi="on">
<div dir="ltr" trbidi="on">
<div dir="ltr" trbidi="on">
<br />
<u style="font-weight: bold;">Problem 1:</u> Convert ( 2 5 A )<sub>16</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= 2 5 A</span></sub><br />
<span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> ↑</span><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> ↑</span><br />
<span style="font-size: x-small;">MSD</span> <span style="font-size: x-small;">LSD</span></div>
<br />
<b>= 2 x 16<sup>2</sup> + 5 x 16<sup>1</sup> + <span style="color: red;">A</span> x 16<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= 2 x 256 + 5 x 16 + <span style="color: red;">10</span> x 1</b><br />
<b><br />
</b><br />
<b>= 512 + 80 + 10</b><br />
<b><br />
</b><br />
<b>= 602</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( 2 5 A )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 6 0 2 )<sub>10</sub></span></b></div>
<br />
<hr />
<br />
<div dir="ltr" trbidi="on">
<u style="font-weight: bold;">Problem 2:</u> Convert ( 2 0 D 0 )<sub>16</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= 2 0 D 0</span></sub><br />
<span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> ↑</span><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> ↑</span><br />
<span style="vertical-align: sub;"><span style="font-size: x-small;">MSD</span> <span style="font-size: x-small;"> LSD</span></span></div>
<br />
<b>= 2 x 16<sup>3</sup> + 0 x 16<sup>2</sup> + <span style="color: red;">D</span> x 16<sup>1</sup></b><b>+ 0 x 16<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= 2 x 4096 + 0 x 256 + <span style="color: red;">13</span> x 16 </b><b>+ 0 x 1</b><br />
<b><br />
</b><br />
<b>= 8192 + 0 + 208 </b><b>+ 0</b><br />
<b><br />
</b><br />
<b>= 8400</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( 2 0 D 0 )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 8 4 0 0 )<sub>10</sub></span></b><br />
<span style="color: #38761d; font-size: x-small;"><b><br />
</b></span><br />
<hr />
<div dir="ltr" trbidi="on">
<u style="font-weight: bold;"><br class="Apple-interchange-newline" />Problem 3:</u> Convert ( F F F F )<sub>16</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= F F F F </span></sub><br />
<span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> ↑</span><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> ↑</span><br />
<span style="vertical-align: sub;"><span style="font-size: x-small;">MSD</span> <span style="font-size: x-small;">LSD</span></span></div>
<br />
<b>= <span style="color: red;">F</span> x 16<sup>3</sup> + <span style="color: red;">F</span> x 16<sup>2</sup> + <span style="color: red;">F</span> x 16<sup>1</sup></b><b>+ <span style="color: red;">F</span> x 16<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= <span style="color: red;">15</span> x 4096 + <span style="color: red;">15</span> x 256 + <span style="color: red;">15</span> x 16 </b><b>+ <span style="color: red;">15</span> x 1</b><br />
<b><br />
</b><br />
<b>= 61440 + 3840 + 240 </b><b>+ 15</b><br />
<b><br />
</b><br />
<b>= 65535</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( F F F F )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 6 5 5 3 5 )<sub>10</sub></span></b><br />
<b><span style="color: #38761d;"><sub><br />
</sub></span></b><br />
<hr />
<div dir="ltr" trbidi="on">
<u style="font-weight: bold;"><br />
</u><br />
<u style="font-weight: bold;">Problem 4:</u> Convert ( A B C 0 )<sub>16</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= A B C 0</span></sub><br />
<span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="background-color: white; color: #222222; line-height: 18px;"> </span></div>
<b>= <span style="color: red;">A</span> x 16<sup>3</sup></b><b>+ <span style="color: red;">B</span> x 16<sup>2</sup></b><b>+ <span style="color: red;">C</span> x 16<sup>1</sup></b><b>+ 0 x 16<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= <span style="color: red;">10</span> x 4096 </b><b>+ <span style="color: red;">11</span> x 256</b><b>+ <span style="color: red;">12</span> x 16 </b><b>+ 0 x 1</b><br />
<b><br />
</b><br />
<b>= 40960 + 2816 + 192 + 0 </b><br />
<b><br />
</b><br />
<b>= 43968</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( A B C 0 )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 4 3 9 6 8 )<sub>10</sub></span></b></div>
</div>
<p></p><p><br /></p>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-5935365629686399532023-02-28T12:52:00.000-08:002023-02-28T12:52:10.203-08:00Difference between octal and hexadecimal<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCRQ-THIAhxonvO3SW8baPQgYJWTpKDshFOu37-UXcrYEHduUIUJBySpAAJIxoRFAPE24C7l6b2YLWCxxvnOKJKUG5Oha1PcGsZKVWQiz1cyK5RJItrmBR_0opvaC4O5G7-UyvkZ6V6tPTFhVaBWvjEDkT2ohMzak967DDUBoTbtWn-FKwl9OxN3Iq/s1024/octal-vs-hexadecimal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Difference between Octal and Hexadecimal" border="0" data-original-height="512" data-original-width="1024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCRQ-THIAhxonvO3SW8baPQgYJWTpKDshFOu37-UXcrYEHduUIUJBySpAAJIxoRFAPE24C7l6b2YLWCxxvnOKJKUG5Oha1PcGsZKVWQiz1cyK5RJItrmBR_0opvaC4O5G7-UyvkZ6V6tPTFhVaBWvjEDkT2ohMzak967DDUBoTbtWn-FKwl9OxN3Iq/w640-h320/octal-vs-hexadecimal.jpg" title="Difference between Octal and Hexadecimal" width="640" /></a></div><br /><p></p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">We have already studied the octal number system and hexadecimal number system and worked on few solved examples to understand the representation of octal numbers and the representation of hexadecimal numbers.</p><span id="more-161" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></span><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Octal-vs-Hexadecimal-Comparison" style="box-sizing: inherit;">Octal vs Hexadecimal Comparison</span></h2><figure class="wp-block-table" style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-x: auto; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><table style="border-collapse: collapse; border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-spacing: 0px; border-style: solid; border-width: 1px 0px 0px 1px; box-sizing: inherit; margin: 0px 0px 1.5em; width: 95%;"><thead style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><th class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; font-weight: 700; padding: 8px; text-align: center;">Hexadecimal Numbers</th><th class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; font-weight: 700; padding: 8px; text-align: center;">Octal Numbers</th></tr></thead><tbody style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">It uses 16 different symbols or digits for representing<span> </span><a class="rank-math-link" href="https://www.schoolelectronic.com/number-systems/#hexadecimal-number-system" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">hexadecimal numbers</a>, [0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F].</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Octal numbers use only 8 symbols or digits to represent all the octal numbers. Therefore, it can have digits from 0 to 7 only.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">The radix or base for hexadecimal numbers is 16.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">The radix or the base for octal number is 8.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Easier to represent and remember large numbers.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Easy to represent using octal number system but difficult to remember large numbers.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Example of Hexadecimal number: FF (Equivalent to Two hundred and fifty-five in decimal)</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Example of Binary number: 377 (Equivalent to Two hundred and fifty-five in decimal)</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">It takes 4 bits or 4 Binary digits to represent a single Hexadecimal digit.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">It takes only 3 bits or 3 Binary digits to represent an Octal digit.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Since the hexadecimal number system uses 16 digits, the arithmetic and logical operations could become complex.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">On the other hand, the Octal number system uses a lesser number of digits (8). This makes performing arithmetic and logic operations easy compared to the hexadecimal number system.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Representing large decimal numbers in the hexadecimal number system is easier.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Representing large decimal numbers in octal becomes difficult and large.</td></tr></tbody></table><figcaption style="box-sizing: inherit;">octal vs hexadecimal</figcaption></figure><p> </p>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-72765073442188507572023-02-28T12:49:00.000-08:002023-02-28T12:49:14.095-08:00Introduction & Importance of Digital electronics<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKdlxVUhSAPnCtuA_ZqYzK4LTVPF2xoErdQ5YR43Id5Zw5_Haupy-1XukIWtljPrNGWL6AJ8-g7IHdk_F0hnxEu4PAAfF1SR_rfON2vCtrmzM3lk0xk4Rw8J0P_FzI04nv02D92K4B_bUv1sACp0ZO4w38R0C-4Z_E5thVegEoktyh98rzgI2rVpsw/s1024/importance-advantages-digital-electronics.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Introduction & Importance of Digital electronics" border="0" data-original-height="512" data-original-width="1024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKdlxVUhSAPnCtuA_ZqYzK4LTVPF2xoErdQ5YR43Id5Zw5_Haupy-1XukIWtljPrNGWL6AJ8-g7IHdk_F0hnxEu4PAAfF1SR_rfON2vCtrmzM3lk0xk4Rw8J0P_FzI04nv02D92K4B_bUv1sACp0ZO4w38R0C-4Z_E5thVegEoktyh98rzgI2rVpsw/w640-h320/importance-advantages-digital-electronics.jpg" title="Introduction & Importance of Digital electronics" width="640" /></a></div><br /><p><br /></p><div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><div class="lwptoc_i" style="background: rgb(250, 250, 250); box-sizing: inherit; color: #333333; display: inline-block; padding: 14px 18px 18px; text-align: left;"><div class="lwptoc_header" style="box-sizing: inherit; margin-bottom: 6px;"><b class="lwptoc_title" style="box-sizing: inherit; font-weight: 700;">Contents</b></div><div class="lwptoc_items lwptoc_items-visible" style="box-sizing: inherit; font-size: 15.3px;"><div class="lwptoc_itemWrap" style="box-sizing: inherit;"><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 0px;"><a href="https://www.schoolelectronic.com/2012/01/importance-advantages-of-digtial.html#Introduction-to-Digital-Electronics" style="border: 0px !important; box-shadow: none !important; box-sizing: inherit; color: #3175e4; text-decoration: none !important; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Introduction to Digital Electronics</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/2012/01/importance-advantages-of-digtial.html#Importance-of-Digital-electronics" style="border: 0px !important; box-shadow: none !important; box-sizing: inherit; color: #3175e4; text-decoration: none !important; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Importance of Digital electronics</span></a></div></div></div></div></div><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Today, We will begin with a short introduction to digital electronics and learn more about<span> </span><a class="rank-math-link" href="https://www.schoolelectronic.com/analog-vs-digital/" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">analog and digital circuits</a><span> </span>in future posts. Before we get started with the formal introduction, I think some questions would have already started running through your mind. Alright, I will put down the question in a better way.</p><span id="more-336" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></span><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Introduction-to-Digital-Electronics" style="box-sizing: inherit;">Introduction to Digital Electronics</span></h2><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">I hope everyone till today would have used or listened to the word ‘digital’ at least once. Well, If you do not remember, the following will definitely remind you.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br style="box-sizing: inherit;" />“I wanna buy a new<span> </span><strong style="box-sizing: inherit; font-weight: 700;">digital camera</strong>.”<br style="box-sizing: inherit;" />“Look at the signboard. It’s a digital display.”<br style="box-sizing: inherit;" />“Hooray! I got a new<span> </span><strong style="box-sizing: inherit; font-weight: 700;">digital watch</strong><span> </span>for my birthday .”</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Technically, all these devices are called digital circuits. The term digital means performing operations on digits(0,1,3,….. etc.) or using these digits for producing information in a form that humans can understand.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Most digital circuits use a binary number system(which has only 2 digits, i.e., 0’s and 1’s), but we will not worry about number systems at this point.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Different authors organize the chapters differently. I always feel starting the course with digital electronics will help the students to feel comfortable with the course. Digital electronics will put the students in a better position to understand electronics because they can relate to the things that exist today.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">I will also try to give examples that can help relate the concepts that you learn with the day-to-day activities.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">At the same time, I will also try to demonstrate some simple experiments that can be done at home as and when we come across various concepts.</p><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Importance-of-Digital-electronics" style="box-sizing: inherit;">Importance of Digital electronics</span></h2><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Earlier, Logic circuits were built using bulky and unreliable components such as transistors, resistors, and vacuum tubes, etc. These components existed individually, and circuits built using these components did not perform as expected, mainly due to the interconnections issues that were common in these circuits. The development of integrated circuits played a significant role in solving the problems of logic circuits. These integrated circuits facilitated to place of a large number of transistors and on a single chip.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><strong style="box-sizing: inherit; font-weight: 700;">Easy to Design:<span> </span></strong>The advent of integrated circuit technology has made it easier to design digital circuits. Today, the designer is not required to know the basic operation of various components such as capacitors, transistors, etc., which involves complex mathematical calculations. If the designer knows the operations of these components, he always has a better hand over other designers.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><strong style="box-sizing: inherit; font-weight: 700;">Reliability:</strong><span> </span>Once a digital circuit is designed. For a given set of inputs, the circuit always produces the same output at any instant of time, unlike analog circuits, whose outputs vary with variation in the environment.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><strong style="box-sizing: inherit; font-weight: 700;">Highly Flexible:<span> </span></strong>In digital circuits, with the help of the software associated with the underlying digital circuit<strong style="box-sizing: inherit; font-weight: 700;">,</strong><span> </span>we can easily change the functionality of the digital circuit without changing the actual circuit. These circuits are generally referred to as programmable digital circuits(we will discuss this in later chapters).</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><strong style="box-sizing: inherit; font-weight: 700;">Cheaper:</strong><span> </span>The rapid advancements in IC (integrated circuit) technology such as the existing VLSI(Very Large Scale Integration) technology has made it possible to produce highly complex digital circuits at low costs.</p><p></p>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-7458534080423896872023-02-24T11:46:00.000-08:002023-02-24T11:46:41.398-08:00Difference between Analog and Digital circuits<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvywgcV4LYdufLiolPm5zDeKMtEH7wLQMDD2LGe_KXqMvzY7PTt-pWmW9zlVjX_OQiINitBKjcBGtqU3tvJbqRbdVWN0dMfBoUTA8yjYstEWoHSOo_T8cfg5J_sT3zXL9IDGonfnRYuOQ/s1600/s.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="difference between analog and digital circuits" border="0" data-original-height="720" data-original-width="1280" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvywgcV4LYdufLiolPm5zDeKMtEH7wLQMDD2LGe_KXqMvzY7PTt-pWmW9zlVjX_OQiINitBKjcBGtqU3tvJbqRbdVWN0dMfBoUTA8yjYstEWoHSOo_T8cfg5J_sT3zXL9IDGonfnRYuOQ/s640/s.jpg" title="difference between analog circuits and digital circuits" width="640" /></a></div><div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><div class="lwptoc_i" style="background: rgb(250, 250, 250); box-sizing: inherit; color: #333333; display: inline-block; padding: 14px 18px 18px; text-align: left;"><div class="lwptoc_header" style="box-sizing: inherit; margin-bottom: 6px;"><b class="lwptoc_title" style="box-sizing: inherit; font-weight: 700;">Content</b><span class="lwptoc_toggle" style="box-sizing: inherit; font-size: 13.6px; margin-left: 4px; white-space: nowrap;"><span> <br /></span></span></div><div class="lwptoc_items lwptoc_items-visible" style="box-sizing: inherit; font-size: 15.3px;"><div class="lwptoc_itemWrap" style="box-sizing: inherit;"><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 0px;"><a href="https://www.schoolelectronic.com/2012/01/difference-between-analog-and-digital.html#Analog-signal-Example" style="border: 0px none; box-shadow: none; box-sizing: inherit; color: #3175e4; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Analog signal Example</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/2012/01/difference-between-analog-and-digital.html#Digital-Signal-Example" style="border: 0px none; box-shadow: none; box-sizing: inherit; color: #3175e4; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Digital Signal Example</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/2012/01/difference-between-analog-and-digital.html#Analog-Circuits-vs-Digital-Circuits" style="border: 0px none; box-shadow: none; box-sizing: inherit; color: #3175e4; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Analog Circuits vs Digital Circuits</span></a></div></div></div></div></div><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;">The fundamental difference between analog and digital circuits is the type of inputs these circuits take in and the type of output signals these circuits operate on to generate the final output.</b></p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;">Analog circuits<span> </span></b>operate or work with continuous-valued signals or continuously varying signals, and these signals are commonly referred to as analog signals. Example of an analog signal is sound, light, etc.</p><span id="more-89" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></span><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Analog-signal-Example" style="box-sizing: inherit;">Analog signal Example</span></h2><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh84RuIREaJJCDrHjmnxhiZPxc7NoOaPMY9AyrPxLsDFRDvlLeevfAP-6_Tvbx85VlPdEP7V4l0PBIkFRLE6v8OgJdyjAFJvraZEABOVy5rEIBkuD-t_8VxkgKwack2taKRiRtLUXYZLm1V7dEBmB1jHUzQneXEwJYmpQ1wnt67ZEdtXrkW9AzBKGEq/s308/example-of-analog-signal.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="example of an analog signal" border="0" data-original-height="268" data-original-width="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh84RuIREaJJCDrHjmnxhiZPxc7NoOaPMY9AyrPxLsDFRDvlLeevfAP-6_Tvbx85VlPdEP7V4l0PBIkFRLE6v8OgJdyjAFJvraZEABOVy5rEIBkuD-t_8VxkgKwack2taKRiRtLUXYZLm1V7dEBmB1jHUzQneXEwJYmpQ1wnt67ZEdtXrkW9AzBKGEq/s16000/example-of-analog-signal.jpg" /></a></div><br /><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;">Digital circuits</b><span> </span>operate or work on signals whose values exist at two levels only or have only two values, i.e., 0’s (zeros) and 1’s (ones) similar to the Binary number system. These signals are commonly referred to as digital signals. At any given instant, the value of a digital signal can be either high (1) or low(0).</p><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Digital-Signal-Example" style="box-sizing: inherit;">Digital Signal Example</span></h2><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-97Bo7Bm83VGA_Yjg8g0ChfTA7XOjyTqhuDYTiM2mPV3c-rTP9YN8sG0-7FjAC1rzpzoO1yeHEEWYuT2Bpi48DVYuuX4WfrPTU0JK6Xi_zZ5JNVr0iR0NOh2vNboGcuOk9yeuVFRreIZemxhi9bYwyK2N12Df0l6Hdd9qFDSooeG_oV0FJwEOvnJ4/s347/digital-signal-example.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="Digital Signal example" border="0" data-original-height="247" data-original-width="347" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-97Bo7Bm83VGA_Yjg8g0ChfTA7XOjyTqhuDYTiM2mPV3c-rTP9YN8sG0-7FjAC1rzpzoO1yeHEEWYuT2Bpi48DVYuuX4WfrPTU0JK6Xi_zZ5JNVr0iR0NOh2vNboGcuOk9yeuVFRreIZemxhi9bYwyK2N12Df0l6Hdd9qFDSooeG_oV0FJwEOvnJ4/w320-h228/digital-signal-example.jpg" title="Digital signal" width="320" /></a></div><br /><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;">Analog circuits are difficult to design and manufacture since most of the design and manufacturing processes involved are manual. In addition to this,</b><span> </span>employing automation techniques for designing these analog circuits fail to do the job efficiently.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">On the other hand,<span> </span><b style="box-sizing: inherit; font-weight: 700;">digital circuits</b><span> </span>are easy to design since Circuit designers can apply automation techniques at various circuit design levels. This involves minimum human interaction.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Analog circuits can process the input analog signal directly using the analog electronic components and produce an output signal. No conversion of input signals is required before processing, i.e., the input signal is analog. An analog circuit directly performs various logical operations and produces an analog output that humans can easily understand.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">In<span> </span><b style="box-sizing: inherit; font-weight: 700;">digital circuits</b>, the input signals are converted from analog to digital form before it is processed, i.e., the digital circuit is capable of processing digital signals only and produces an output which is again converted back from digital to analog signals so that the output gives meaning full results that humans can understand.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">In <b style="box-sizing: inherit; font-weight: 700;">analog circuits</b>, since there are no conversions involved at the input or the output side, there is no loss of information available for processing.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Due to the conversion process at the input side(analog to digital) and the output side (digital to analog), some information is lost during the conversion process.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The human resources available to design analog circuits are meager. This results in a long time to market for the finished products.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;">Analog circuits</b><span> </span>are mostly custom made and lacks flexibility.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><b style="box-sizing: inherit; font-weight: 700;">Digital circuits</b><span> </span>have high degree of flexibility.</p><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Analog-Circuits-vs-Digital-Circuits" style="box-sizing: inherit;">Analog Circuits vs Digital Circuits</span></h2><figure class="wp-block-table" style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-x: auto; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><table style="border-collapse: collapse; border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-spacing: 0px; border-style: solid; border-width: 1px 0px 0px 1px; box-sizing: inherit; margin: 0px 0px 1.5em; width: 95%;"><tbody style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Analog Circuits</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Digital Circuits</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">These circuits operate on continuous valued signals(commonly referred to as analog signals).</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">These circuits operate on signals that exist only at two levels i.e. 0’s and 1’s (binary number system).</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Analog circuits are difficult to design since each component has to be placed by hand as automation techniques for designing these circuits fail to do the job efficiently.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">On the other hand digital circuits are easy to design since automation technique can be applied at various levels of circuit design. This involves minimum human interaction.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">No conversion of input signals are required before processing i.e. input signal is analog, the circuit directly performs various logical operations and produces an analog output.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">In digital circuits, the input signals are converted from analog to digital form before it is processed, i.e. the digital circuit is capable of processing digital signals only, and produces output which is again converted back from digital to analog signals so that the output gives meaning full results that can be understood by humans.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">In analog circuits, since there are no conversions involved at the input or at the output side there is no loss of information that is available for processing.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Due to the conversion process at the input side(analog to digital) and at the output side, some amount of information is lost during the conversion process.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">The man power available to design analog circuits is very low, this results in long time to market the finished products.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">The available man power to design digital circuits is significantly large compared to that of analog circuit designers.</td></tr><tr style="box-sizing: inherit;"><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Analog circuits are mostly custom made and lacks flexibility.</td><td class="has-text-align-center" data-align="center" style="border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-style: solid; border-width: 0px 1px 1px 0px; box-sizing: inherit; padding: 8px; text-align: center;">Digital circuits have high degree of flexibility.</td></tr></tbody></table><figcaption style="box-sizing: inherit;">Analog Circuits vs Digital Circuits</figcaption></figure><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Note: Even though digital electronics have taken over analog electronics, We still cannot eliminate analog electronics because, in the real world, we use only analog signals, i.e., humans can understand only analog signals (not 0’s and 1’s).<br style="box-sizing: inherit;" />Can you imagine talking to your friend in terms of 0’s and 1’s (sounds funny)?<br style="box-sizing: inherit;" />With all the digital circuits designed to interact with the real world, the digital circuits must have an analog interface.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px; orphans: 2; overflow-wrap: break-word; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">A simple example would be your computer keyboard.<br style="box-sizing: inherit;" />Each time you type something on the keyboard, you see the corresponding key on the monitor. What happens under your keyboard is: As soon as you type a key, a set of 0’s and 1’s are sent to the processing unit, which is in turn given to the monitor which can understand only 0’s and 1’s the monitor then displays the set of 0’s and 1’s in the form you can understand (English).</p></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-8365036957057429202023-02-24T11:33:00.000-08:002023-02-24T11:33:11.011-08:00what are the similarities and differences between the binary and decimal systems?<div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></div><div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></div><div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHVmlZwN6MkVZHyxf3irh1FLUNMMB9R8Ge53UlSeEBNPcoNWwHSYwFA2h-N5qhEQeE2Zq8X_tgzQVaPH7ULnwMQ_zZG4zw5mruEOeHtwlvu69ldq-2rYkMK5as-ZQmxw2TFkwRUSmDZoT56qUZp5rSb7r6MXCuyGcfLxEwzf7A9Xg-d05Qwh9QWpef/s1024/decimal-vs-binary.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="similarities and differences between the binary and decimal systems" border="0" data-original-height="512" data-original-width="1024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHVmlZwN6MkVZHyxf3irh1FLUNMMB9R8Ge53UlSeEBNPcoNWwHSYwFA2h-N5qhEQeE2Zq8X_tgzQVaPH7ULnwMQ_zZG4zw5mruEOeHtwlvu69ldq-2rYkMK5as-ZQmxw2TFkwRUSmDZoT56qUZp5rSb7r6MXCuyGcfLxEwzf7A9Xg-d05Qwh9QWpef/w640-h320/decimal-vs-binary.jpg" width="640" /></a></div></div><div class="lwptoc lwptoc-autoWidth lwptoc-baseItems lwptoc-light lwptoc-notInherit" data-lwptoc-initialized="1" data-smooth-scroll-offset="24" data-smooth-scroll="1" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 16px 0px 32px; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /><div class="lwptoc_i" style="background: rgb(255, 255, 255); border: 1px solid rgb(173, 173, 173); box-sizing: inherit; color: #333333; display: inline-block; padding: 14px 18px 18px; text-align: left;"><div class="lwptoc_header" style="box-sizing: inherit; margin-bottom: 6px;"><b class="lwptoc_title" style="box-sizing: inherit; font-weight: 700;">Contents</b></div><div class="lwptoc_items lwptoc_items-visible" style="box-sizing: inherit; font-size: 15.3px;"><div class="lwptoc_itemWrap" style="box-sizing: inherit;"><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 0px;"><a href="https://www.schoolelectronic.com/decimal-vs-binary/#Similarities-between-Binary-and-Decimal-systems" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Similarities between Binary and Decimal systems</span></a></div><div class="lwptoc_item" style="box-sizing: inherit; margin-top: 2px;"><a href="https://www.schoolelectronic.com/decimal-vs-binary/#Differences-between-Binary-and-Decimal-Systems" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;"><span class="lwptoc_item_label" style="box-sizing: inherit;">Differences between Binary and Decimal Systems</span></a></div></div></div></div></div><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"> </p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">In this post, we will do a quick comparison of decimal vs binary number systems, highlighting all the similarities and differences between the two number systems for better understanding of their use case.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">We are familiar with the decimal number system or the decimal numeration system since we use it every day for paying bills, grocery shopping, bank transactions, etc.,. In the decimal number system, we represent or express a given decimal number in Units, tens, hundreds, thousands, etc.,</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">On the other hand, our computers and other digital devices which we use every day make use of the binary number system to communicate, perform arithmetic and logical operations.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The decimal number uses 10 digits to represent different values whereas the Binary number uses only 2 digits (0 & 1) to represent any binary number.</p><span id="more-175" style="-webkit-text-stroke-width: 0px; background-color: white; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></span><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">We will further advance the discussion, and see<span> </span><b style="box-sizing: inherit; font-weight: 700;">what are the main similarities and differences between the binary and decimal systems.</b></p><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Similarities-between-Binary-and-Decimal-systems" style="box-sizing: inherit;">Similarities between Binary and Decimal systems</span></h2><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Firstly, the binary and decimal systems can represent or express numbers with both integer parts and fractional parts equally. So any given number, for example, the number 14, in decimal system it is (14)<sub style="box-sizing: inherit; font-size: 12.75px; height: 0px; line-height: 0; position: relative; top: 0.5ex; vertical-align: baseline;">10</sub><span> </span>and in the binary system it is expressed as (1110)<sub style="box-sizing: inherit; font-size: 12.75px; height: 0px; line-height: 0; position: relative; top: 0.5ex; vertical-align: baseline;">2</sub>. Here, subscript 10 & 2 are the radix of respective number systems.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Another important similarity between the binary and decimal system is that the value of a given digit (in a decimal number) or a given bit (in binary number) is determined by the position of the decimal digit from the decimal point or position of binary bit from the binary point. The farthest digit or binary bit from the decimal/binary point has the largest weight.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Example for the decimal system: 623.54 – the left-most digit starting from the decimal point (1) has the largest weight and the rightmost digit from the decimal point has the lowest weight or value(4).</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Example for the binary system: 101.010 – the leftmost bit starting from the binary point(1) has the largest weight and the rightmost bit starting from the binary point towards the right has the least weight or value(0).</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">In addition to this, a similarity between binary and decimal systems worth mentioning is that the binary system is also capable of performing all the arithmetic operations like addition, subtraction, multiplication, and division just like we do in the decimal number system.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Let us list out all the similarities between binary and decimal systems in a tabular form to remember them easily.</p><figure class="wp-block-table" style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-x: auto; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><table style="border-collapse: collapse; border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-spacing: 0px; border-style: solid; border-width: 1px 0px 0px 1px; box-sizing: inherit; margin: 0px 0px 1.5em; width: 95%;"><thead style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><th style="border: 1px solid; box-sizing: inherit; font-weight: 700; padding: 0.5em;">Binary System</th><th style="border: 1px solid; box-sizing: inherit; font-weight: 700; padding: 0.5em;">Decimal System</th></tr></thead><tbody style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The binary system can represent integer binary numbers as well as fractional binary numbers.</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The decimal system can also represent decimal numbers containing both integer and fraction components.</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The value or weight of a bit depends on the position of the bit from the radix point.</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The value/weight of a digit in a given decimal number also depends on the position of the digit from the decimal point.</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Example of binary number with integer and fractional part: 101.010 (Five and Twenty Five hundredths)</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Example of Decimal number: 5.25 (Five and Twenty Five hundredths)</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;"><a class="rank-math-link" href="https://www.schoolelectronic.com/number-systems/#representation-of-a-decimal-number" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">Representation of Decimal number & decimal number fraction.</a></td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;"><a class="rank-math-link" href="https://www.schoolelectronic.com/number-systems/#representation-of-binary-number" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">Representation of Binary number and binary fraction.</a></td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">All arithmetic operations like addition, subtraction, multiplication & division can be performed on binary numbers.<br style="box-sizing: inherit;" /><br style="box-sizing: inherit;" /></td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Addition, subtraction, multiplication & division arithmetic operations can be performed on decimal numbers.<br style="box-sizing: inherit;" /></td></tr></tbody></table><figcaption class="wp-element-caption" style="box-sizing: inherit;">Decimal vs Binary – Similarities between Binary and Decimal Systems</figcaption></figure><h2 style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 30px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 600; letter-spacing: normal; line-height: 1.2em; margin: 0px 0px 20px; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span id="Differences-between-Binary-and-Decimal-Systems" style="box-sizing: inherit;">Differences between Binary and Decimal Systems</span></h2><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">We see that Binary system and decimal system are nothing but two different number systems or numeration systems based on the number of digits used by each system. Both binary and decimal systems differ at various levels.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The fundamental difference between binary and decimal systems is the number of digits used to represent any given number. The binary system uses only 2 digits (0s & 1s) to represent binary numbers while the decimal system uses 10 digits from 0 to 9 (0,1,2,3,4,5,6,7,8,9) to represent any decimal number integer or fraction.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The binary system which uses only 2 digits is also referred to as base-two system, while the decimal system utilizing 10 digits is known as base-ten system.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLq6Mmw4GMHaLeypaXEZ5DbsEWCjg__2VZxK6zIogXfQu5iusXpF1hPosGJ4ojMV1g2MOGHrXeJa66uWlY1vpSbqz4HziYlsIBOb8Z9zoVJ-p-9QT5rLoVaJZG8d1EsHlxRTy73hocYwA8mF5GbsJw23UUxyiJXKNv8ARZcLgYCS5w30upP_G1mC19/s849/binary-number-system.png" style="margin-left: 1em; margin-right: 1em;"><img alt="Decimal vs Binary - Binary number system" border="0" data-original-height="229" data-original-width="849" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLq6Mmw4GMHaLeypaXEZ5DbsEWCjg__2VZxK6zIogXfQu5iusXpF1hPosGJ4ojMV1g2MOGHrXeJa66uWlY1vpSbqz4HziYlsIBOb8Z9zoVJ-p-9QT5rLoVaJZG8d1EsHlxRTy73hocYwA8mF5GbsJw23UUxyiJXKNv8ARZcLgYCS5w30upP_G1mC19/w400-h108/binary-number-system.png" title="Binary number system" width="400" /></a></div><br /><figure class="wp-block-image size-large" style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; height: auto; letter-spacing: normal; margin: 0px 0px 1.5em; max-width: 100%; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><figcaption class="wp-element-caption" style="box-sizing: inherit; font-size: 13px; margin-bottom: 1em; margin-top: 0.5em; text-align: center;">Binary Number System</figcaption></figure><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The units in the binary system (0s and 1s) are known as bits which is more familiar in the computer world. The units in the decimal number system (0 to 9) are called digits.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW79ZMuhy37hE_y1xCaYQYt51YjDahFS7z9exXBtVfD4o6VNGDq5QyRdo-dl6e3aQRajZ5CCsY-eQ50Y5gjCceyr0_oKYd42sk07wBiyUNHNncWsrhSpdsw2tvI-n72IQs-pk5YFPpKPDWT6efSMhiaofPJY_cBV4Tn7uXRziXgCU2bQbXAQOyTxSH/s928/decimal-number-system.png" style="margin-left: 1em; margin-right: 1em;"><img alt="Decimal vs Binary - decimal number system" border="0" data-original-height="298" data-original-width="928" height="128" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW79ZMuhy37hE_y1xCaYQYt51YjDahFS7z9exXBtVfD4o6VNGDq5QyRdo-dl6e3aQRajZ5CCsY-eQ50Y5gjCceyr0_oKYd42sk07wBiyUNHNncWsrhSpdsw2tvI-n72IQs-pk5YFPpKPDWT6efSMhiaofPJY_cBV4Tn7uXRziXgCU2bQbXAQOyTxSH/w400-h128/decimal-number-system.png" title="Decimal number system" width="400" /></a></div><figure class="wp-block-image size-large" style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; height: auto; letter-spacing: normal; margin: 0px 0px 1.5em; max-width: 100%; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><figcaption class="wp-element-caption" style="box-sizing: inherit; font-size: 13px; margin-bottom: 1em; margin-top: 0.5em; text-align: center;">Decimal Number System</figcaption></figure><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The radix used in the binary system is 2, the radix used in the decimal system is 10. In other words, we can also say that in the binary system the values or weights are expressed as the power of 2 and in the decimal system, the values are expressed as the power of 10.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The radix point in the binary system is called a Binary Point and the radix point in the decimal system is referred to as Decimal Point.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">In a binary system, the left-most bit which has the largest weight is referred to as the Most Significant Bit(MSB), and the rightmost bit from the binary point which has the least weight is referred to as Lease Significant Bit (LSB). In the decimal system, the left-most digit with the highest weight is called a Most significant digit (MSD) and the rightmost digit with the least weight is called a Least Significant Digit (LSD).</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">It is easier to learn the various arithmetic and logical operations in the binary system when compared to the decimal system since the binary system has only 2 digits (0 and 1).</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">On the contrary, it becomes tedious to remember and work with large binary numbers as compared to large decimal numbers.</p><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Example: 65536 in decimal system is easy to remember than 10000000000000000 in binary system.</p><figure class="wp-block-table" style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px 0px 1.5em; orphans: 2; overflow-x: auto; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><table style="border-collapse: collapse; border-color: rgba(0, 0, 0, 0.1); border-image: initial; border-spacing: 0px; border-style: solid; border-width: 1px 0px 0px 1px; box-sizing: inherit; margin: 0px 0px 1.5em; width: 95%;"><thead style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><th style="border: 1px solid; box-sizing: inherit; font-weight: 700; padding: 0.5em;">Decimal Numbers</th><th style="border: 1px solid; box-sizing: inherit; font-weight: 700; padding: 0.5em;">Binary Numbers</th></tr></thead><tbody style="box-sizing: inherit;"><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Decimal numbers consist of combination ten digits or values from 0 to 9 (0,1,2,3,4,5,6,7,8,9).</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Binary numbers are expressed or represented by the combination of only 2 digits or values 0 (zero) and 1 (one).</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The Radix for decimal number is 10, i.e., all the digits in a decimal number are expressed in terms of powers of 10.</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The Radix for binary number is 2, i.e., all the digits or values in a binary number are expressed in terms of powers of 2.</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Example of decimal number: 25 (Twenty Five)</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Example of Binary number: 11001 (Twenty Five)</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;"><a class="rank-math-link" href="https://www.schoolelectronic.com/number-systems/#representation-of-a-decimal-number" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">Representation of Decimal number & decimal number fraction.</a></td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;"><a class="rank-math-link" href="https://www.schoolelectronic.com/number-systems/#representation-of-binary-number" style="box-sizing: inherit; color: #1b78e2; text-decoration: none; transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;">Representation of Binary number and binary fraction.</a></td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">It is easier to represent and work with large decimal numbers.</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">It is pretty difficult to remember and work with large binary numbers as the number of bits required to represent increases drastically as the numbers grow.</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The radix point is called a decimal point.</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">The radix point is referred to as a binary point.</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">In Decimal number system, we have Units, Tenths, Hundredths, Thousandths commonly referred to as decimal units.</td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">In Binary number system, we have bits.<br style="box-sizing: inherit;" />Group of 4 bits is called a nibble,<br style="box-sizing: inherit;" />Group of 8 bits is called a Byte<br style="box-sizing: inherit;" />Group of 16 Bits is called a word.</td></tr><tr style="box-sizing: inherit;"><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Applications<br style="box-sizing: inherit;" />Most common and used in everyday life.<br style="box-sizing: inherit;" />Used in all Financial transactions, banking operations.<br style="box-sizing: inherit;" /><br style="box-sizing: inherit;" /></td><td style="border: 1px solid; box-sizing: inherit; padding: 0.5em;">Applications<br style="box-sizing: inherit;" />Most widely used for performing arithmetic and logical operations in all digital circuits.<br style="box-sizing: inherit;" /></td></tr></tbody></table><figcaption class="wp-element-caption" style="box-sizing: inherit;">Decimal vs Binary – Difference between Binary and Decimal Systems</figcaption></figure><p style="-webkit-text-stroke-width: 0px; background-color: white; border: 0px none; box-sizing: inherit; color: #212121; font-family: Helvetica; font-size: 17px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin: 0px; orphans: 2; padding: 0px; text-align: start; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Note : Even though decimal numbers and binary numbers are different, the set of rules for addition, subtraction, multiplication and division applicable to decimal numbers is also applicable to binary numbers. But the way the these operations are performed is slightly different which we will learn in detail later.</p>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-33850388684089162752013-11-15T02:48:00.010-08:002020-12-04T04:00:20.974-08:00Hexadecimal to binary short conversion method<div dir="ltr" style="text-align: left;" trbidi="on">
<br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifYRALBczGgiBg4xeIghWLEuza7HXp1sW6Bep4SRNcbBkZLyQuvaujHFgphbQfpZRRklAndN1G3oY0e46DEYb_MLCkh1N0ATKzHmBiRKZKEhBzXDXB-NForFOWxPh42nhKtWRBg8rXLU0/s1024/hexadecimal-to-binary-conversion.webp" style="margin-left: auto; margin-right: auto;"><img alt="Hexadecimal to Binary" border="0" data-original-height="512" data-original-width="1024" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifYRALBczGgiBg4xeIghWLEuza7HXp1sW6Bep4SRNcbBkZLyQuvaujHFgphbQfpZRRklAndN1G3oY0e46DEYb_MLCkh1N0ATKzHmBiRKZKEhBzXDXB-NForFOWxPh42nhKtWRBg8rXLU0/w400-h200/hexadecimal-to-binary-conversion.webp" title="How to convert Hexadecimal to binary" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Hexadecimal to Binary<br /></td></tr></tbody></table><br /><div dir="ltr" style="text-align: left;" trbidi="on"><br />
In this post, we will learn the basic steps to convert a hexadecimal number to binary number.<br />
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There are two methods to convert hexadecimal to binary, one is the short method and another is long method. Here we will discuss only the steps relating to the short method and the long method of conversion will be covered in later post.<br />
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<li>The hexadecimal number system has 16 digits starting from 0 to F, where the largest hexadecimal digit is (F)<sub>16</sub>.</li>
<li>Referring to the hexadecimal to binary conversion table, we see that the binary equivalent of the largest hexadecimal digit (F)<sub>16</sub> is (1111)<sub>2</sub> and minimum of four binary digits(bits) are required to represent the largest hexadecimal digit in the binary system.</li>
<li>In order to convert the given hexadecimal number to binary number, we convert each hexadecimal digit into four-bit binary number beginning from the right most hexadecimal digit towards the leftmost digit (MSD).</li>
<li>At the end, the four-bit binary numbers are combined to form the single binary number equivalent to the given hexadecimal number. </li>
</ol>
The above steps are explained with an example for better understanding:<br />
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<u><b>Example 1:</b></u><b>Convert hexadecimal number (FA98)<sub>16</sub> to binary number (?)<sub>2</sub></b> <br />
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<span style="color: #3d85c6;"><u><b>Step 1:</b></u> </span>Each digit from the given hexadecimal number is written down leaving small space between each digit as shown below<br />
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<b>Hexadecimal Number -> F A 9 8</b><br />
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<span style="color: #3d85c6;"><u><b>Step 2:</b></u></span> Referring to the <a href="https://www.schoolelectronic.com/2013/10/Relationship-between-decimal-binary-octal-and-hexadecimal-number-systems.html">conversion table</a> to find the binary equivalents of each hexadecimal digit.</div>
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The binary equivalents are:</div>
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F-1111</div>
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A-1010</div>
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9-1001</div>
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8-1000 </div>
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Write down the four-bit binary numbers below each hexadecimal digit as shown below:</div>
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<b> Hexadecimal Number -> <span style="color: red;">F</span> A 9 <span style="color: blue;"><span style="color: #660000;">8</span></span></b></div>
<b> <span style="color: red;">↓</span> <span style="color: #6aa84f;">↓</span> <span style="color: #990000;">↓</span> </b><b><span style="color: #990000;">↓</span></b><br />
<b> Binary Number -> <span style="color: red;">1111</span> <span style="color: #6aa84f;">1010</span> <span style="color: #990000;">1001 1000</span></b><br />
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<span style="color: #990000;"><span style="color: #0b5394;">Hence, the binary equivalent of the given hexadecimal number is <b>(1111101010011000)<sub>2</sub></b></span></span><b> </b></div>
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School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-75380828502033442372013-11-12T22:19:00.007-08:002020-12-03T04:38:16.672-08:00Octal to binary conversion method with example<div dir="ltr" style="text-align: left;" trbidi="on">
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" 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In this post, we will learn the method used to convert a given integer octal number to its equivalent in the binary number system<br />
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The octal number system has a base of 8 i.e. the number of digits in the octal number system is eight(8) starting from 0 to 7.<br />
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<li>The highest digit in the octal number system is <b>(7)<sub>8</sub></b>, from the <a href="https://www.schoolelectronic.com/2013/10/Relationship-between-decimal-binary-octal-and-hexadecimal-number-systems.html">number system conversion table</a> we can see that <b>(111)<sub>2</sub></b> is the binary equivalent of the highest octal digit and three binary digits(bits) are required to represent the highest octal digit.</li>
<li>In the <b>octal to binary conversion method</b>, we will convert each digit from the given octal number into three bit binary number starting from the right most octal digit(LSD) to the left most digit(MSD) and at the end combine each three bit binary number to form the binary equivalent of given octal number.</li>
<li>The steps involved in the octal to binary conversion is explained with example below:</li>
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<u><b>Example-1</b></u>: Convert octal number <b>(375)<sub>8</sub></b> to binary number <b>(?)<sub>2</sub></b> <br />
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<span style="color: #3d85c6;"><u><b>Step 1:</b></u> </span></h2>
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<span style="color: #3d85c6;"> </span>Write down each digit from the given octal number leaving some space between each octal digit as shown below</div>
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<b>Octal Number -> 3 7 5</b></div>
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<span style="color: #3d85c6;"><u><b>Step 2:</b></u></span> </h2>
If you have memorized the binary equivalents of all the octal digits this step becomes very easy, otherwise you can still refer the <a href="https://www.schoolelectronic.com/2013/10/Relationship-between-decimal-binary-octal-and-hexadecimal-number-systems.html">conversion table</a> to find the binary equivalents of each octal digit.<br />
Represent each octal digit with its binary equivalent as shown below<br />
We know that,<br />
Binary equivalent of octal digit 3 is 011<br />
Binary equivalent of octal digit 7 is 111<br />
Binary equivalent of octal digit 5 is 101</div>
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Write down the three bit number below each octal digit as shown below:</div>
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<b> Octal Number -> <span style="color: red;">3</span> <span style="color: #6aa84f;">7</span> <span style="color: blue;"> <span style="color: #660000;">5</span></span></b></div>
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<b> <span style="color: red;">↓</span> <span style="color: #6aa84f;">↓</span> <span style="color: #990000;">↓</span> </b><br />
<b>Binary Number -> <span style="color: red;">011</span> <span style="color: #6aa84f;">111</span> <span style="color: #990000;">101</span></b><br />
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<span style="color: #3d85c6;"><u><b>Step 3:</b></u></span> </h2>
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<span style="color: #990000;"><span style="color: #0b5394;">Group the binary equivalents of each octal digit starting from right most digit to obtain the complete binary equivalent of the given octal number.</span></span><br />
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<span style="color: #990000;"><span style="color: #0b5394;">Hence, the binary equivalent of the given octal number is <b>(11111101)<sub>2</sub></b></span></span></h3>
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<span style="color: #990000;"><span style="color: #0b5394;"><b><sub> </sub></b></span></span></h3>
<u><b>Example-2</b></u>: Convert octal number <b>(634)<sub>8</sub></b> to binary number <b>(?)<sub>2</sub></b> <br />
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<span style="color: #3d85c6;"><u><b>Step 1:</b></u> </span></h2>
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Write down each digit from the given octal number as shown below</div>
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<b>Octal Number -> 6 3 4</b></div>
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<span style="color: #3d85c6;"><u><b>Step 2:</b></u></span> </h2>
Represent each octal digit with its binary equivalent as shown below<br />
We know that,<br />
Binary equivalent of octal digit 6 is 110<br />
Binary equivalent of octal digit 3 is 011<br />
Binary equivalent of octal digit 4 is 100<br />
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Write down the three bit binary equivalents below each octal digit as shown below:</div>
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<b> Octal Number -> 6 <span style="color: #6aa84f;">3</span> <span style="color: blue;"> <span style="color: #660000;">4</span></span></b></div>
<div style="text-align: center;">
<b> <span style="color: red;">↓</span> <span style="color: #6aa84f;">↓</span> <span style="color: #990000;">↓</span> </b><br />
<b>Binary Number -> <span style="color: red;">110</span> <span style="color: #6aa84f;">011</span> <span style="color: #990000;">100</span></b><br />
<br />
<div style="text-align: left;">
<h2>
<span style="color: #3d85c6;"><u><b>Step 3:</b></u></span> </h2>
<br />
<span style="color: #990000;"><span style="color: #0b5394;">Group
the binary equivalents of each octal digit starting from right most
digit to obtain the complete binary equivalent of the given octal
number.</span></span><br />
<span style="color: #990000;"><span style="color: #0b5394;"> </span></span><br />
<h3 style="text-align: left;">
<span style="color: #990000;"><span style="color: #0b5394;">Hence, the binary equivalent of the given octal number is <b>(110011100)<sub>2</sub></b></span></span> </h3>
</div>
</div>
<h3 style="text-align: left;">
<span style="color: #990000;"><span style="color: #0b5394;"><b><sub> </sub></b></span></span> </h3>
</div>
</div>
<ol style="text-align: left;">
</ol>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-20740895589481848252013-10-22T10:25:00.004-07:002020-12-03T05:22:10.942-08:00Decimal Binary Octal & hexadecimal Conversion Table<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4bFIqjYtYARU58F1yg1o-WXyqrfzeI0kAziHFHIDJIlA7uY7Gk9H0t2yL2mmWOpXrFRmW1jX5PFjTY0j0ieMI1qj0FW0bKWVuWzqOM3XLAH5chPp2wlWPsNjaZ8EAP6M4xaUAjQ1aACA/s1024/decimal-binary-octal-hexadecimal-conversion-table.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Decimal, binary, octal, hexadecimal conversion table" border="0" data-original-height="512" data-original-width="1024" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4bFIqjYtYARU58F1yg1o-WXyqrfzeI0kAziHFHIDJIlA7uY7Gk9H0t2yL2mmWOpXrFRmW1jX5PFjTY0j0ieMI1qj0FW0bKWVuWzqOM3XLAH5chPp2wlWPsNjaZ8EAP6M4xaUAjQ1aACA/w320-h160/decimal-binary-octal-hexadecimal-conversion-table.jpg" width="320" /></a></div><br /> </div><div dir="ltr" style="text-align: left;" trbidi="on">The earlier posts covered the detailed procedure step by step for converting a given number from one number system to another with exams.<br />
<br />
The below table gives the equivalent numbers in the four number systems that we will be using in basic electronics.<br />
<br />
<a name='more'></a><br />
<br />
This <b>conversion table</b> is nothing but a simple cheat sheet for performing mathematical and logical operations on the various number systems that we came across earlier, similar to the multiplication tables (from 1 to 20) that we asked to memorize in lower grade math class in order to perform complex multiplication and division operations faster.<br />
<br />
This table will act as a simple speed up bonus to perform the mathematical operations among the number systems faster.<br />
<br />
<table border="1" style="border-collapse: collapse; border: 1px solid rgb(223, 223, 223); font-family: "Roboto", sans-serif; height: 486px; text-align: center; width: 633px;">
<tbody>
<tr style="background-color: #efefef; padding: 10px;">
<th>Decimal<br />
<span style="font-size: 12px; font-weight: normal;">Base 10</span></th>
<th>Binary<br />
<span style="font-size: 12px; font-weight: normal;">Base 2</span></th>
<th>Octal<br />
<span style="font-size: 12px; font-weight: normal;">Base 8</span></th>
<th>Hexadecimal<br />
<span style="font-size: 12px; font-weight: normal;">Base 16</span></th>
</tr>
<tr>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>1</td>
<td>1</td>
<td>1</td>
<td>1</td>
</tr>
<tr>
<td>2</td>
<td>10</td>
<td>2</td>
<td>2</td>
</tr>
<tr>
<td>3</td>
<td>11</td>
<td>3</td>
<td>3</td>
</tr>
<tr>
<td>4</td>
<td>100</td>
<td>4</td>
<td>4</td>
</tr>
<tr>
<td>5</td>
<td>101</td>
<td>5</td>
<td>5</td>
</tr>
<tr>
<td>6</td>
<td>110</td>
<td>6</td>
<td>6</td>
</tr>
<tr>
<td>7</td>
<td>111</td>
<td>7</td>
<td>7</td>
</tr>
<tr>
<td>8</td>
<td>1000</td>
<td>10</td>
<td>8</td>
</tr>
<tr>
<td>9</td>
<td>1001</td>
<td>11</td>
<td>9</td>
</tr>
<tr>
<td>10</td>
<td>1010</td>
<td>12</td>
<td>A</td>
</tr>
<tr>
<td>11</td>
<td>1011</td>
<td>13</td>
<td>B</td>
</tr>
<tr>
<td>12</td>
<td>1100</td>
<td>14</td>
<td>C</td>
</tr>
<tr>
<td>13</td>
<td>1101</td>
<td>15</td>
<td>D</td>
</tr>
<tr>
<td>14</td>
<td>1110</td>
<td>16</td>
<td>E</td>
</tr>
<tr>
<td>15</td>
<td>1111</td>
<td>17</td>
<td>F</td>
</tr>
<tr>
<td>16</td>
<td>10000</td>
<td>20</td>
<td>10</td>
</tr>
</tbody></table>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-19302775089418365832013-09-28T02:04:00.002-07:002020-11-22T13:32:50.812-08:00Decimal to hexadecimal fraction Conversion<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWfr1NVDo07TUre6QyMP1ZC3OYQn_0Qd60Aaw0zw0ax61NOcquhSY9hl24in7DQ8RF5_kj11nGdJ0Sv5p1VTbdLZ_S6QquVGgq8KnTpQeTKCMWnAy9uTXzHFlpFj4_wSC4wBgCK7BCvI8/s1600/DF1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 2em;"> <img alt="How to convert decimal fraction to hexadecimal fraction" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWfr1NVDo07TUre6QyMP1ZC3OYQn_0Qd60Aaw0zw0ax61NOcquhSY9hl24in7DQ8RF5_kj11nGdJ0Sv5p1VTbdLZ_S6QquVGgq8KnTpQeTKCMWnAy9uTXzHFlpFj4_wSC4wBgCK7BCvI8/s1600/DF1.png" title="" /></a></div>
<br />
<br />
In the earlier post we discussed the integer conversion of a given decimal number to its equivalent hexadecimal number.<br />
<br />
The method involved in the conversion of fractional decimal number to fraction hexadecimal number is different, in this post we will only concentrate on the fractional conversion.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<a name='more'></a><br />
<br />
<br />
<span style="color: #990000;"><b>Procedure</b></span><br />
<br />
The steps for the conversion are given below:<br />
<br />
<b>Successive multiplication </b>is used to convert a given fractional decimal number to its equivalent hexadecimal fraction.<br />
<ol style="text-align: left;">
<li>Here the given decimal fraction is successively multiplied by the base of the target number system (16, here it is hexadecimal system). </li>
<li>During each multiplication iteration, the product generated will have a carry (integer part of the product) and a fractional part.</li>
<li>The carry obtained at each multiplication step becomes a numeral in the hexadecimal fraction.</li>
<li>The fractional part of the product is again multiplied by base 16 in the next step and the process is
repeated until the <b>fractional part becomes zero</b> or the <b>number of
multiplication iteration equals the number of digits after
the decimal point in the given decimal fraction</b>.</li>
<li>Weights are assigned for the carry obtained at each multiplication step in the increasing order starting from the first multiplication step to the last step, such that the carry obtained in the first multiplication
iteration is the <b>most significant bit (MSD)</b> after the decimal point and the carry obtained in the last multiplication iteration is the <b>least significant bit (LSD)</b></li>
<li>This procedure is illustrated in the following example.</li>
</ol>
<br />
<br />
<br />
<br />
<u><b>Ex1:</b></u> Convert (0.0628)<sub>10</sub> decimal fraction to hexadecimal fraction (?)<sub>16</sub> using successive multiplication method<br />
<u><br /></u>
<u><b>1st Multiplication Iteration</b></u><br />
<br />
Multiply 0.0628 by 16<br />
<div style="text-align: center;">
0.0628 x 16 = 1.0048(Product) Fractional part=0.0048 Carry=1 <b>(MSD)</b><br />
<br />
<div style="text-align: left;">
<u><b><br /></b></u></div>
</div>
<u><b>2nd Multiplication Iteration</b></u><br />
<br />
Multiply 0.0048 by 16<br />
0.0048 x 16 = 0.0768(Product) Fractional part = 0.0768 Carry = 0 <br />
<br />
<u><b>3rd Multiplication Iteration</b></u><br />
<br />
Multiply 0.0768 by 16<br />
0.0768 x 16 = 1.2288(Product) Fractional part = 0.2288 Carry = 1 <br />
<div style="text-align: center;">
<br />
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<u><b>4th Multiplication Iteration</b></u></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Multiply 0.2288 by 16</div>
<div style="text-align: left;">
0.2288 x 16 = 3.6608(Product) Fractional part = 0.6608 Carry = 3 <b>(LSD)</b> </div>
<div style="text-align: left;">
</div>
</div>
<div style="text-align: center;">
<br />
<div style="text-align: left;">
Here the fractional part doesn't become zero but we obtain required number of significant digits after the decimal point. Thus we stop the multiplication iteration and assign the weights to the digits obtained in each multiplication step in the increasing order starting from the 1st multiplication step to last multiplication step.<br />
<br /></div>
</div>
Carry from the 1st multiplication iteration becomes <b>MSB </b>and carry from 4th iteration becomes <b>LSB</b> after the decimal point.<br />
<br />
Hence, the fractional hexadecimal number of the given decimal fraction <br />
<span style="color: #cc0000;"> <b>(0.0628)<sub>10</sub></b> is (</span><b><span style="color: #cc0000;">0.1013)<sub>16</sub></span>.</b></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-15988982835173952932013-09-22T11:11:00.009-07:002020-11-22T13:49:14.137-08:00Decimal to Hexadecimal<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRWpkrv_84XV8DEYHkOHLZguw_snXDwNXu1mJ7FvkHjc1B5T0SHwWOFScmmIip3CEOQi_CVSd-bIV0AYbYzlAr_a3HdKsdmoA3g3FzlJhqOf0_k0f0HxlQPW6E7pmzkFb5P503vaIhQyE/s1600/se.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1.5em;"><img alt="how to convert decimal to hexadecimal" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRWpkrv_84XV8DEYHkOHLZguw_snXDwNXu1mJ7FvkHjc1B5T0SHwWOFScmmIip3CEOQi_CVSd-bIV0AYbYzlAr_a3HdKsdmoA3g3FzlJhqOf0_k0f0HxlQPW6E7pmzkFb5P503vaIhQyE/s1600/se.png" title="" /></a><br />
In this post, we will go through the detailed steps for converting a given number from <a href="https://www.schoolelectronic.com/2012/01/decimal-number-system.html">decimal number system</a><a href="https://www.schoolelectronic.com/2012/01/decimal-number-system.html"> </a>to it equivalent in the <a href="https://www.schoolelectronic.com/2012/01/hexadecimal-number-system.html">hexadecimal number system</a>. Here we will only concentrate on conversion of integer decimal number and steps to convert fractional decimal to hexadecimal will be discussed in a separate post. </div>
<div style="text-align: left;">
<br />
This conversion also follows the same method of successive division of the given number by the radix or the base of the target number system(here hexadecimal) i.e 16.<br />
<div style="text-align: right;">
</div>
<a name='more'></a></div>
<div style="text-align: left;">
<br />
<br />
<br />
<u><b></b></u><br />
<h2><span style="font-family: Times,"Times New Roman",serif;"><span style="font-size: large;"> <span style="color: #990000;"><u>How to Convert Decimal to Hexadecimal</u></span></span></span></h2><span face=""Helvetica Neue",Arial,Helvetica,sans-serif"><span style="font-size: small;"><br /></span></span></div>
<ol style="text-align: left;">
<li>Integer part of the given decimal number is successively divided by
the radix(base) hexadecimal number system 16 until quotient becomes <b>zero(0).</b></li>
<li>The reminder obtained for each division, becomes a digit in the hexadecimal number. </li>
<li><b> </b>The remainders obtained at each division step are assigned weights in the hexadecimal system in the decreasing order starting from the remainder obtained in the last division step to the remainder obtained in the first division step.</li>
<li>The reminder in the last division iteration has the highest weight <b>(MSD) which becomes the left most digit </b>and the reminder obtained in the first division iteration has the lowest weight <b>(LSD) which becomes the right most digit </b>in the hexadecimal number.</li>
<li>The procedure is illustrated in the example below:</li>
</ol>
<br />
<span style="color: #3d85c6;"><u><b>Ex1:</b></u> </span>Convert (5049)<sub>10</sub> decimal number to octal number (?)<sub>16</sub> using successive division method<br />
<u><br /></u>
<u><b>1st Division Iteration</b></u><br />
<br />
Divide 5049 by 16<br />
<div style="text-align: center;">
5049 ÷ 16 = 315(Quotient) Reminder=9<br />
<br />
<div style="text-align: left;">
<u><b><br /></b></u>
<u><b><br /></b></u></div>
</div>
<u><b>2nd Division Iteration</b></u><br />
<br />
Divide 315 by 16<br />
<div style="text-align: center;">
315 ÷ 16 = 19(Quotient) Reminder=B </div>
<br />
<br />
<br />
<u><b>3rd Division Iteration</b></u><br />
<br />
Divide 19 by 16<br />
<div style="text-align: center;">
19 ÷ 16 = 1(Quotient) Reminder=3 </div>
<br />
<br />
<u><b>4th Division Iteration</b></u><br />
<br />
Divide 1 by 16<br />
<div style="text-align: center;">
1 ÷ 16 = 0(Quotient) Reminder=1 </div>
<br />
<br />
Remainder from the last division iteration (1) becomes <b>MSD </b>and reminder from 1st iteration (9) becomes <b>LSD</b>.<br />
<br />
<span style="color: #0b5394;">Hence, the hexadecimal equivalent of the decimal number <b>5049</b> is (<b>13B9).</b></span></div>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-25025654369503378922013-08-20T04:56:00.005-07:002020-12-03T07:18:42.801-08:00Decimal to octal number<div dir="ltr" style="text-align: left;" trbidi="on"> <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJcyZCcVftv8GbidnLmf68nt2NYsNbxMzt8_sINecqj27pS4yvsPa7mf-r76hqS4ti2evLwJbLR5ee-oEGGjuDBZxInUuERb7aeopDY2WpTAiKEm0PyJ690bgoIZcbDFJjBdyGWN2h0dQ/s1024/decimal-to-octal.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="Decimal to octal conversion" border="0" data-original-height="512" data-original-width="1024" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJcyZCcVftv8GbidnLmf68nt2NYsNbxMzt8_sINecqj27pS4yvsPa7mf-r76hqS4ti2evLwJbLR5ee-oEGGjuDBZxInUuERb7aeopDY2WpTAiKEm0PyJ690bgoIZcbDFJjBdyGWN2h0dQ/w320-h160/decimal-to-octal.jpg" title="How to convert decimal to octal" width="320" /></a></div><br /></div><div dir="ltr" style="text-align: left;" trbidi="on">Decimal to octal conversion can be performed using multiple methods. Some methods are more widely used than the others.<br /></div><div dir="ltr" style="text-align: left;" trbidi="on"> <br /></div><div dir="ltr" style="text-align: left;" trbidi="on">In earlier post, we have seen the procedure for converting a given decimal number to its equivalent binary number.<br />
<br />
In this post, we will see the step-by-step procedure to convert given decimal number to its equivalent in the octal number system.<br />
<br />
As discussed earlier, we will implement the same division method used earlier, to convert decimal to octal and all the steps will be very much similar to the steps shown in decimal to binary conversion except for the change in the radix from 2 to 8 since here the target number system is octal number system.<br />
<br />
<a name='more'></a><br /><br />
<ol style="text-align: left;">
<li>Integer part of the given decimal number is successively divided by the radix(base) of the target number system 8(octal) until we reach a stage where the quotient becomes <b>zero(0).</b></li>
<li>The reminder obtained at the end of each division step, becomes a part of the octal number. </li>
<li><b> </b>The reminders that obtained at the end of each step are assigned weights in the octal number system starting from the reminder obtained at the last division iteration to the first division iteration in decreasing order.</li>
<li>The reminder in the last division iteration has the highest weight <b>(MSD) </b>and the reminder obtained in the first division iteration has the lowest weight <b>(LSD) </b>in the octal number system.</li>
<li>The procedure is illustrated in the example below:</li></ol><p> </p><h2 style="text-align: left;">Decimal to Octal Conversion Example <br /></h2><ol style="text-align: left;">
</ol>
</div><div dir="ltr" style="text-align: left;" trbidi="on"></div><div dir="ltr" style="text-align: left;" trbidi="on"></div><div dir="ltr" style="text-align: left;" trbidi="on"></div><div dir="ltr" style="text-align: left;" trbidi="on"></div><div dir="ltr" style="text-align: left;" trbidi="on"></div><div dir="ltr" style="text-align: left;" trbidi="on"><br />
<u><b>Ex1:</b></u> Convert (83)<sub>10</sub> decimal number to octal number (?)<sub>8</sub> using division method<br />
<u><br /></u>
<u><b>1st Division Iteration</b></u><br />
<br />
Divide 83 by 8<br />
<div style="text-align: center;">
83 ÷ 8 = 10(Quotient) Reminder:3<br />
<br />
<div style="text-align: left;">
<u><b><br /></b></u></div>
</div>
<u><b>2nd Division Iteration</b></u><br />
<br />
Divide 10 by 8<br />
<div style="text-align: center;">
10 ÷ 8 = 1(Quotient) Reminder=2 </div>
<br />
<u><b>3rd Division Iteration</b></u><br />
<br />
Divide 1 by 8<br />
<div style="text-align: center;">
1 ÷ 8 = 0(Quotient) Reminder=1 </div>
<br />
<br />
<div style="text-align: center;">
</div>
Remainder from the last division iteration becomes <b>MSD </b>and reminder from 1st iteration becomes <b>LSD</b>.<br />
<br />
Hence, the octal equivalent of the decimal number <b>83</b> is (<b>123).</b></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-83060563197242334472013-04-16T01:13:00.003-07:002020-12-07T12:58:04.082-08:00Decimal fraction to binary fraction conversion<div dir="ltr" style="text-align: left;" trbidi="on">
<ol style="text-align: left;">
<li><b>Successive multiplication method</b> is used to convert a given fractional decimal number to its equivalent binary fraction.</li>
<li>In this method of conversion the fractional part of the given decimal number is multiplied by 2 (i.e. the radix of binary number system). </li>
<li>The product obtained has an integer part and fractional part, the integer part here is also referred as carry.</li>
<li>The carry that we obtain at each multiplication iteration becomes a digit in the fractional binary number.</li>
<li>The fractional part obtained is again multiplied and the process is repeated until the fractional part becomes zero or the number of multiplication iteration equals the number of significant digits after the decimal point in the given fractional decimal number.</li>
<li>The carry that we obtain at each stage are taken from first iteration to the last iteration to form the numerals in the fractional binary number i.e. the carry obtained in the first multiplication iteration is the <b>most significant bit (MSB)</b> after the decimal point and the carry obtained in the last multiplication iteration is the <b>least significant bit (LSB)</b></li>
<li>This procedure is illustrated in the following example.</li>
</ol>
<br />
<a name='more'></a><br />
<br />
<br />
<u><b>Ex1:</b></u> Convert (0.625)<sub>10</sub> decimal number to binary number (?)<sub>2</sub> using successive multiplication method</div><div dir="ltr" style="text-align: left;" trbidi="on"><b>[0.625 as a fraction in binary from decimal]</b><br />
<u><br /></u>
<u><b>1st Multiplication Iteration</b></u><br />
<br />
Multiply 0.625 by 2<br />
<div style="text-align: center;">
0.625 x 2 = 1.25(Product) Fractional part=0.25 Carry=1 <b>(MSB)</b><br />
<br />
<div style="text-align: left;">
<u><b><br /></b></u></div>
</div>
<u><b>2nd Multiplication Iteration</b></u><br />
<br />
Multiply 0.25 by 2<br />
<div style="text-align: center;">
0.25 x 2 = 0.50(Product) Fractional part = 0.50 Carry = 0 </div>
<br />
<u><b>3rd Multiplication Iteration</b></u><br />
<br />
Multiply 0.50 by 2<br />
<div style="text-align: center;">
0.50 x 2 = 1.00(Product) Fractional part = 1.00 Carry = 1 <b>(LSB)</b> <br />
</div>
<div style="text-align: center;">
<br />
<div style="text-align: left;">
The fractional part in the 3rd iteration becomes zero and hence we stop the multiplication iteration.</div>
<div style="text-align: left;">
</div>
</div>
Carry from the 1st multiplication iteration becomes <b>MSB </b>and carry from 3rd iteration becomes <b>LSB</b>.<br />
<br />
Hence, the fractional binary number of the given fractional decimal number <b>(0.625)<sub>10</sub></b> is (<b>0.101)<sub>2</sub>.</b><br />
<ol style="text-align: left;">
</ol>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-5954963471061746922013-02-25T02:33:00.000-08:002013-11-17T20:34:04.473-08:00Convert decimal to binary using division method<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTK313wlrnFdD2odJHlEPJw5Ayh6J61_Xgu1w_q0H1phyphenhyphenRmHqmsoXl5cgSrixVEMU7q_2L09rFAVcyjZR9xVdh-H2fKkVzNS2u1dRCSy3-YNMXu1uFz_gfXXQoA87B6Mi4QeGRD6zcCzE/s1600/decimal2bin.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 2em;"><img alt="How to convert decimal to binary" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTK313wlrnFdD2odJHlEPJw5Ayh6J61_Xgu1w_q0H1phyphenhyphenRmHqmsoXl5cgSrixVEMU7q_2L09rFAVcyjZR9xVdh-H2fKkVzNS2u1dRCSy3-YNMXu1uFz_gfXXQoA87B6Mi4QeGRD6zcCzE/s1600/decimal2bin.png" title="How to convert decimal to binary" /></a></div>
<ol style="text-align: left;">
<li>Division method is used to convert only integer part of a decimal number to its equivalent in binary number system.</li>
<li>In this method the integer part of the decimal number is continuously divided until we reach a stage where the quotient becomes zero.</li>
<li>The reminder that we obtain at each division iteration becomes the value of the weights or the digits in the binary number system.</li>
<li>The reminders that we obtain are taken from the last step to first step i.e. the last reminder obtained during the division iteration is the most significant digit (<b>MSD</b>) and the first reminder the we obtained is the least significant digit in the binary number system.</li>
<li>You will understand the procedure better with the following illustrative example. </li>
</ol>
<br />
<br />
<br />
<u><b>Ex1:</b></u> Convert (32)<sub>10</sub> decimal number to binary number (?)<sub>2</sub> using division method<br />
<u><br /></u>
<u><b>1st Division Iteration</b></u><br />
<br />
Divide 32 by 2<br />
<div style="text-align: center;">
32 ÷ 2 = 16(Quotient) Reminder:0<br />
<br />
<div style="text-align: left;">
<u><b><br /></b></u></div>
</div>
<u><b>2nd Division Iteration</b></u><br />
<br />
Divide 16 by 2<br />
<div style="text-align: center;">
16 ÷ 2 = 8(Quotient) Reminder=0 </div>
<br />
<u><b>3rd Division Iteration</b></u><br />
<br />
Divide 8 by 2<br />
<div style="text-align: center;">
8 ÷ 2 = 4(Quotient) Reminder=0 </div>
<br />
<u><b>4th Division Iteration</b></u><br />
<br />
Divide 4 by 2<br />
<div style="text-align: center;">
4 ÷ 2 = 2(Quotient) Reminder=0<br />
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<u><b>5th Division Iteration</b></u></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Divide 2 by 2</div>
2 ÷ 2 = 1(Quotient) Reminder=0<br />
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<u><b>6th Division Iteration</b></u></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
Divide 1 by 2</div>
1 ÷ 2 = 0(Quotient) Reminder=1<br />
<br />
<br /></div>
Remainder from the last division iteration becomes <b>MSD </b>and reminder from 1st iteration becomes <b>LSD</b>.<br />
<br />
Hence, the binary equivalent of the decimal number <b>32</b> is (<b>100000).</b></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-1957010198796265182012-10-03T21:12:00.000-07:002019-08-02T16:04:44.360-07:00Difference between binary and hexadecimal<head>
<meta name="description" content="Major differences between hexadecimal numbers and binary numbers and its applications" />
</head>
<table border="1" bordercolor="dfdfdf" style="border-collapse: collapse; height: 800px; margin-top: -10px; text-align: center;"><tbody>
<tr> <th bgcolor="efefef">Hexadecimal Numbers</th> <th bgcolor="efefef" width="370">Binary Numbers</th> </tr>
<tr> <td>Hexadecimal numbers make use of 16 symbols 0 to 9 and additional symbols (A, B, C, D, E, F). Hexadecimal numbers were introduced with the purpose to represent binary numbers in a more human readable form. </td><td>Binary numbers make use of only 2 symbols (0, 1) to represent any number and it becomes a tedious job to express large numbers.<br />
</td></tr>
<tr bgcolor="ffffdf"> <td>The radix or base for hexadecimal number is 16 and each symbol in a hexadecimal number is expressed as power of 16. </td><td>The <b>radix </b>for binary numbers is 2 and also termed as base 2 numbers.</td></tr>
<tr> <td>It is easy and more human readable to represent number in hexadecimal system.</td><td>Large numbers represented in binary system are not in a human readable form.</td></tr>
<tr> <td><b>Example of Hexadecimal number</b> : FF (Equivalent to Two hundred and fifty five in decimal)</td><td><b>Example of Binary number</b> : 11111111 (Equivalent to Two hundred and fifty five in decimal)</td></tr>
<tr bgcolor="ffffdf"> <td><b><u>Applications</u> </b><br />
<ul>
<li>Used for representing addresses of memory locations in microprocessors and assembly language programming.</li>
</ul>
</td><td><br />
<b><u>Applications</u></b><br />
<ul>
<li>All the digital circuits use binary numbers at the lowest level of interaction and to perform logical operations.</li>
</ul>
<br />
<ul>
</ul>
</td></tr>
</tbody></table>
<div>
<b><br />
</b></div>
<div>
<br /></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-27363165175829417462012-10-02T21:05:00.001-07:002019-08-02T15:58:31.878-07:00Difference between octal and decimal numbers<head>
<meta name="description" content="Difference between decimal number system and octal number system, octal numbers vs decimal numbers" />
</head>
<table border="1" bordercolor="dfdfdf" style="border-collapse: collapse; height: 800px; margin-top:-10px; text-align: center; "><tbody>
<tr> <th bgcolor="efefef">Octal Numbers</th> <th bgcolor="efefef" width="370">Decimal Number</th> </tr>
<tr> <td>Octal numbers are made up of 8 distinct symbols or digits from 0 to 7 ( 0, 1, 2, 3, 4, 5, 6, 7). </td><td>Decimal numbers are made up of 10 distinct symbols or digits ranging from 0 to 9 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).</td></tr>
<tr bgcolor="ffffdf"> <td>The <b>radix </b>for octal number is <b>8</b> i.e all the digits in an octal number are expressed as powers of 8.</td><td>The <b>radix </b>for decimal number is <b>10</b> i.e all the digits or values in a decimal number are expressed as of powers of 10.</td></tr>
<tr> <td><b>Example of octal number</b> : 7777 ( Equivalent to four thousand ninety five in decimal )</td><td><b>Example of Decimal number</b> : 4095 ( Four thousand ninety five)</td></tr>
<tr bgcolor="ffffdf"> <td><b><u>Applications of octal numbers</u> </b><br />
<ul>
<li>The usage of octal number system has decreased since the introduction of hexadecimal number system, but still octal numbers are used in some programming languages.</li>
</ul>
</td><td><br />
<b><u>Applications of decimal numbers</u></b><br />
<ul>
<li>Decimal numbers are used in all financial institutions and most commonly used in our day to day activities.</li>
</ul>
<br />
<ul>
</ul>
</td></tr>
</tbody></table>
<div>
<b><br />
</b></div>
<div>
<br /></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-22836986980048261372012-09-30T21:11:00.003-07:002020-11-16T05:11:39.824-08:00Difference between Hexadecimal and decimal numbers<table border="1" bordercolor="dfdfdf" style="border-collapse: collapse; height: 800px; margin-top: -10px; text-align: center;"><tbody>
<tr> <th bgcolor="efefef">Hexadecimal Numbers</th> <th bgcolor="efefef" width="370">Decimal Numbers</th> </tr>
<tr> <td>Hexadecimal numbers make use of 16 symbols to represent numbers, it uses the 10 symbols of decimal number system to represent values 0 to 9 and additional 6 symbols (A, B, C, D, E, F) to represent values ( 10, 11, 12, 13, 14, 15) respectively. </td><td>Decimal numbers make use of 10 symbols from 0 to 9 and its combinations to represent different values.</td></tr>
<tr bgcolor="ffffdf"> <td>The <b>radix </b>for Hexadecimal number is <b>16</b> i.e all the digits in a Hexadecimal number are expressed in terms of powers of 16.</td><td>The <b>radix </b>for decimal number is <b>10</b> i.e all the digits or values in a decimal number are expressed in terms of powers of 10.</td></tr>
<tr> <td>Hexadecimal numbers are more human friendly, i.e. large numbers are easier to remember.</td><td>Large decimal numbers are relatively difficult to remember.</td></tr>
<tr> <td><b>Example of Hexadecimal number</b> : FFFF (sixty five thousand five hundred thirty five)</td><td><b>Example of Decimal number</b> : 65535 (sixty five thousand five hundred thirty five)</td></tr>
<tr bgcolor="ffffdf"> <td><b><u>Applications</u> </b><br />
<ul>
<li>Microprocessors and microcontrollers use hexadecimal numbers to represent address of memory locations.</li>
</ul>
</td><td><br />
<b><u>Applications</u></b><br />
<ul>
<li>Most common and used in everyday life.</li>
<li>Used in all Financial transactions, banking operations.</li>
</ul>
<ul>
</ul>
</td></tr>
</tbody></table>
<div>
<b><br />
</b></div>
<div>
<br /></div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-10314868575976107452012-04-29T11:35:00.003-07:002020-12-04T04:03:58.729-08:00Number system conversion<div dir="ltr" style="text-align: left;" trbidi="on">
So far in the previous posts we have discussed about representation of numbers in different number systems. We have also solved example problems step by step and tried some shortcuts as well.<br />
In the following posts we will discuss basic conversion techniques to convert any given number from one number system to another.<br />
<br />
At this point you would ask me "<i>hey why do we need to do this number conversion stuff?</i> ".<br />
This question is absolutly valid becase in electronics the decision on which number system should be used primarily depends on the type of application to put it in a better way lets take an <b>example</b>.<br />
<br />
You are providing your mobile number to one your classmate for instance this is your mobile number <b>(123)-456-0123</b> in the decimal number system and you decide to give it in the binary format as <b>(1111011)-111001000-1111011.</b><br />
However, when you give the same number in decimal format to your computer. The number will be converted to its binary equivalent as shown above and stored.(computer understands only 0's and 1's).<br />
<br />
From the above example we can clearly make out when we require decimal and when we require binary number sytem.<br />
<b> </b><br />
The octal number system and the hexadecimal number system was introduced mainly to make the machine codes more human friendly instead of the 0's and 1's.<br />
The octal number system has fallen back and rarely it finds any use in today's applications. The hexadecimal number system is the most widely used number system today. Modern computers use hexadecimal format for memory addresses and makes it lot more easier to debug when ever the computer throws out an error with a hexadecimal address instead of a long string of 0's and 1's.<br />
<br />
We will start learning the conversions methods from decimal number system as we are more familiar to decimal number sytem. Under the decimal number system conversion we will learn the following conversions<br />
<br />
<ol style="text-align: left;">
<li><a href="https://www.schoolelectronic.com/2013/02/Convert-decimal-to-binary-using-division-method.html">Decimal number system to binary number system</a></li>
<li><a href="https://www.schoolelectronic.com/2013/08/convert-decimal-to-octal-number.html">Decimal number system to octal number system</a></li>
<li><a href="https://www.schoolelectronic.com/2013/09/convert-decimal-to-hexadecimal-number.html">Decimal number system to hexadecimal number system</a></li>
<li><a href="https://www.schoolelectronic.com/2012/01/convert-binary-to-decimal-number.html">Binary number system to decimal number system</a></li>
<li><a href="https://www.schoolelectronic.com/2012/01/convert-octal-to-decimal-number.html">Octal number system to decimal number system</a></li>
<li><a href="https://www.schoolelectronic.com/2012/01/convert-hexadecimal-to-decimal-number.html">Hexadecimal number system to decimal number system</a></li>
</ol>
<b> </b> </div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-3403098512373126302012-01-29T06:20:00.001-08:002020-12-03T05:38:48.140-08:00Convert hexadecimal fraction to decimal fraction<div dir="ltr" style="text-align: left;" trbidi="on">
<span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif" style="background-color: white; color: #222222; line-height: 18px;">Solved examples of Hexadecimal fractions to decimal fraction conversion</span><br />
<div dir="ltr" style="background-color: white; line-height: 18px;" trbidi="on">
<div dir="ltr" style="color: #222222;" trbidi="on">
<br />
<u style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">Problem 1:</u><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif"> Convert ( E F . B 1 )</span><sub style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">16</sub><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif">= ( ? )</span><sub style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">10</sub><br />
<sub style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</sub><br />
<span style="font-family: inherit;"><sub>= <span style="font-size: small;"> E F <b>.</b> B 1</span></sub><br />
<span style="background-color: white;"> ↑</span><span style="background-color: white;"> ↑</span><br />
<span style="vertical-align: sub;">MSD LSD</span></span></div>
<div style="color: #222222;">
<br /></div>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="color: #222222;">= </span><span style="color: red;">E</span><span style="color: #222222;"> x 16</span><sup style="color: #222222;">1</sup><span style="color: #222222;"> + </span><span style="color: red;">F</span><span style="color: #222222;"> x 16</span><sup style="color: #222222;">0</sup><span style="color: #222222;"> . </span><span style="color: red;">B</span><span style="color: #222222;"> x 16</span><sup style="color: #222222;">-1</sup></b><span style="color: #222222;"> </span><b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">+ 1 x 16<sup>-2</sup></b><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif" style="color: #222222;"> </span><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif" style="color: #222222;"> </span><br />
<div style="color: #222222;">
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><sup><br />
</sup></b></div>
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="color: #222222;">= </span><span style="color: red;">14</span><span style="color: #222222;"> x 16 + </span><span style="color: red;">15</span><span style="color: #222222;"> x 1 . </span><span style="color: red;">11</span><span style="color: #222222;"> x ( 1 / 16 )</span></b><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif" style="color: #222222;"> </span><b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">+ 1 x ( 1 / 256 )</b><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif" style="color: #222222;"> </span><b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b><br />
<div style="color: #222222;">
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b></div>
<div style="color: #222222;">
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">= 224 + 15 . ( 0. 6 8 7 5 )</b><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif"> </span><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">+ </b><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> ( 0 . 0 0 3 9 0 6 2 5 )</b><span face=""arial" , "tahoma" , "helvetica" , "freesans" , sans-serif"> </span><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b></div>
<div style="color: #222222;">
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b></div>
<div style="color: #222222;">
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">= 239 + 0. 6914</b></div>
</div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div dir="ltr" trbidi="on">
<b>= 239 . 691406</b></div>
<br />
<br />
<b>Therefore <span style="color: #38761d;"> ( E F . B 1 )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 2 3 9 . 6 9 1 4 0 6 )<sub>10</sub></span></b></div>
<br />
<hr style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" />
<br />
<div dir="ltr" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div dir="ltr" style="color: #222222;" trbidi="on">
<br />
<u style="font-weight: bold;">Problem 2:</u> Convert ( 0.9D9 )<sub>16</sub>= ( ? )<sub>10</sub><br />
<sub><br />
</sub><br />
<sub><span style="font-size: small;">= 0 <b>.</b> 9 D 9</span></sub><br />
<span style="background-color: white;"> ↑</span><span style="background-color: white;"> ↑</span><br />
<span style="vertical-align: sub;">MSD LSD</span></div>
<div style="color: #222222;">
<br /></div>
<b style="color: #222222;">= 0 x 16<sup>0</sup> . 9 x 16<sup>-1</sup></b><span style="color: #222222;"> </span><b><span style="color: #222222;">+ </span><span style="color: red;">D</span><span style="color: #222222;"> x 16</span><sup style="color: #222222;">-2</sup></b><span style="color: #222222;"> </span><b style="color: #222222;">+ 9 x 16<sup>-3</sup></b></div>
<div dir="ltr" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div style="color: #222222;">
<b><sup><br />
</sup></b></div>
<b style="color: #222222;">= 0 x 1 . 9 x ( 1 / 16 )</b><span style="color: #222222;"> </span><b><span style="color: #222222;">+ </span><span style="color: red;">13</span><span style="color: #222222;"> x ( 1 / 256 )</span></b><span style="color: #222222;"> </span><b style="color: #222222;">+ 9 x ( 1 / 4096 )</b><span style="color: #222222;"> </span></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<b>= 0 . (0. 5625)</b> <b>+ (0 . 050781 ) </b> <b>+ </b><b>( 0. 0021972 )</b> </div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<b>= 0 . ( 0 . 6154782 )</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<div dir="ltr" trbidi="on">
<b>= </b><b style="background-color: white;">0 . 6154782</b></div>
<br />
<br />
<b>Therefore <span style="color: #38761d;"> ( 0 . 9 D 9 )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 0 . 6 1 5 4 7 8 2 )<sub>10</sub></span></b></div>
<br />
<hr style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" />
<br />
<br />
<div>
<div dir="ltr" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div dir="ltr" style="color: #222222;" trbidi="on">
<u style="font-weight: bold;">Problem 3:</u> Convert ( BCC.1 0 )<sub>16</sub>= ( ? )<sub>10</sub><br />
<sub><br />
</sub><br />
<span style="font-size: small;"><sub><span style="font-size: small;">= B C C <b>.</b> 1 0</span></sub></span><span style="background-color: white;"> </span><br />
<b style="background-color: white;"><span style="background-color: white; font-weight: normal;"> ↑</span><span style="background-color: white; font-weight: normal;"> ↑</span></b></div>
<div dir="ltr" style="background-color: white; color: #222222;" trbidi="on">
<b><span style="font-weight: normal; vertical-align: sub;"> MSD LSD</span></b><br />
<b><span style="font-weight: normal; vertical-align: sub;"><br />
</span></b></div>
<b style="color: #222222;">= </b><b><span style="color: red;">B</span></b><b style="color: #222222;"> x 16<sup>2 </sup></b><b style="color: #222222;">+ </b><b><span style="color: red;">C</span></b><b style="color: #222222;"> x 16<sup>1 </sup></b><b><span style="color: #222222;">+ </span><span style="color: red;">C</span><span style="color: #222222;"> x 16</span><sup style="color: #222222;">0</sup></b><b style="color: #222222;"> . 1 x 16<sup>-1 </sup></b><b style="color: #222222;">+ 0 x 16<sup>-2</sup></b><span style="color: #222222;"> </span></div>
<div dir="ltr" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div style="color: #222222;">
<b><sup><br />
</sup></b></div>
<b style="color: #222222;">= </b><b><span style="color: red;">11</span></b><b style="color: #222222;"> x 256</b><b><span style="color: #222222;">+ </span><span style="color: red;">12</span><span style="color: #222222;"> x 16</span></b><b style="color: #222222;">+ </b><b><span style="color: red;">12</span></b><b style="color: #222222;"> x 1</b><b style="color: #222222;"> . 1 x ( 1 / 16 )<sup> </sup></b><b style="color: #222222;">+ 1 x ( 1 / 256 )</b><br />
<div style="color: #222222;">
<b><br />
</b></div>
<div style="color: #222222;">
<b>= 2816 + 192 </b><b>+ 12 </b><b> . ( 0 . 0625 )<sup> </sup></b><b>+ </b><b> ( 0 )</b> <b><br />
</b></div>
<div style="color: #222222;">
<b><br />
</b></div>
<div style="color: #222222;">
<b>= 3020</b><b><sup> </sup></b><b> </b><b> . </b> <b>( 0. 0625 )</b> </div>
</div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<div dir="ltr" trbidi="on">
<b>= 3020 . 0625</b></div>
<br />
<br />
<b>Therefore <span style="color: #38761d;"> ( B C C . 1 0 )<sub>16</sub></span></b><b><span style="color: #38761d;"> = ( 3 0 2 0 . 0 6 2 5 )<sub>10</sub></span></b></div>
<br />
<hr style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" />
<br />
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" trbidi="on">
<br class="Apple-interchange-newline" />
<span style="color: #0b5394;"><span style="font-size: small;"><span face=""helvetica neue" , "arial" , "helvetica" , sans-serif">Also read: </span></span></span><a href="https://www.schoolelectronic.com/2013/09/convert-decimal-fraction-to-hexadecimal.html">How to convert decimal fraction to hexadecimal fraction</a></div>
</div>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-30270884026753819572012-01-26T07:04:00.000-08:002012-10-07T21:23:00.240-07:00Hexadecimal fraction representation<div dir="ltr" style="text-align: left;" trbidi="on">
We will discuss in detail about how we can represent the fractional numbers in hexadecimal number system.<br />
<div>
The hexadecimal point or the radix point plays the same role as that of decimal point in decimal number system and octal point in the octal number system i.e. the point that separates the integer part of the hexadecimal digits and fractional hexadecimal number digits.</div>
<div>
<br /></div>
<div>
The procedure is similar to the steps that we followed to represent a decimal fraction and binary fractions.</div>
<div>
<br /></div>
<div>
<br /></div>
<div>
Example 1:<b> (4 1 A . E F 9 )<sub>16</sub></b> is the Hexadecimal equivalent of ( <b>1050 . 883049 )</b> in decimal number system.</div>
<div>
<u style="font-weight: bold;"><br />
</u></div>
<div>
<u style="font-weight: bold;">Step 1:</u></div>
<div>
<br /></div>
<div>
Write down the sequence of hexadecimal positional weights based on the number of digits present in the given hexadecimal number separated by the hexadecimal point as shown below</div>
<div>
<br />
<br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> </span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0 </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-1</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-2</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-3</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← Weights in hexadecimal</b><br />
<table border="1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px; text-align: left;"><tbody>
<tr><td> </td><td> </td><td> </td><td> <b>.</b> </td><td> </td><td> </td><td> </td></tr>
</tbody></table>
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">MSD LSD</span><br />
<br />
<u style="font-weight: bold;">Step 2:</u> Assign the values for each of the weights starting from LSD till the hexadecimal point and again beginning from the hexadecimal point assign the integer hexadecimal values up to the MSD towards far left as done below.<br />
<br />
<br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><br class="Apple-interchange-newline" /> </span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0 </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-1</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-2</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-3</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← Weights in hexadecimal</b><br />
<table border="1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px; text-align: left;"><tbody>
<tr><td> 4 </td><td> 1 </td><td> A </td><td> <b>.</b> </td><td> E </td><td> F </td><td> 9 </td></tr>
</tbody></table>
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">MSD LSD</span></div>
<div>
<br />
<br />
<u style="font-weight: bold;">Step 3:</u> Compute the product of individual hexadecimal digits and its associated individual weights to get the products which looks like the following<br />
<br />
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
9 x <b style="background-color: white;">16 </b><sup style="background-color: white; font-weight: bold;">-1 </sup><sup style="background-color: white;"> </sup><span style="background-color: white;">←</span><b style="background-color: white;"> LSD </b><sup style="background-color: white; font-weight: bold;"> </sup></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
F x <b style="background-color: white;">16 </b><sup style="background-color: white; font-weight: bold;">-2 </sup></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
E x <b style="background-color: white;">16 </b><sup style="background-color: white; font-weight: bold;">-3</sup></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
<sup style="background-color: white; font-weight: bold;"><span style="font-size: small;"> . </span></sup></div>
<div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
<div style="color: #222222;">
A x <b style="background-color: white;">16 </b><sup style="background-color: white; font-weight: bold;">0 </sup></div>
<div style="color: #222222;">
1 x <b style="background-color: white;">16 </b><sup style="background-color: white; font-weight: bold;">1</sup></div>
<div style="color: #222222;">
4 x <b style="background-color: white;">16 </b><sup style="background-color: white; font-weight: bold;">2 </sup><b style="background-color: white;">← MSD </b></div>
<div style="color: #222222;">
<b style="background-color: white;"><br />
</b></div>
<div style="color: #222222;">
<b style="background-color: white;"><br />
</b></div>
<div style="color: #222222;">
<b style="background-color: white;"><u>Step 4:</u> </b><span style="background-color: white;">Determine</span><span style="background-color: white;"> the sum of the individual products separated by the hexadecimal point as illustrated below</span></div>
<div style="color: #222222;">
<span style="background-color: white;"><br />
</span></div>
<div>
<div style="color: #222222;">
<b> 4 x <span style="background-color: white;">16 </span><sup style="background-color: white;">2 </sup>+ 1 x 16<span style="background-color: white;"> </span><sup style="background-color: white;">1 </sup>+ A x 16<span style="background-color: white;"> </span><sup style="background-color: white;">0 </sup>. E x <span style="background-color: white;">16 </span><sup style="background-color: white;">-1</sup></b> + <b>F x <span style="background-color: white;">16 </span><sup style="background-color: white;">-2</sup></b> + <b>9 x <span style="background-color: white;">16 </span><sup style="background-color: white;">-3</sup></b><br />
<b><sup style="background-color: white;"><br />
</sup></b></div>
<div>
<b style="background-color: white; color: #222222;"><sup style="background-color: white;"> </sup></b><b style="background-color: white; color: #222222;">= 4</b><b style="background-color: white; color: #222222;"> x <span style="background-color: white;">16 </span><sup style="background-color: white;">2 </sup>+ 1 x <span style="background-color: white;">16 </span><sup style="background-color: white;">1 </sup>+ </b><b style="background-color: white;"><span style="color: red;">A</span></b><b style="background-color: white; color: #222222;"> x <span style="background-color: white;">16 </span><sup style="background-color: white;">0 </sup>. </b><b style="background-color: white;"><span style="color: red;">E</span></b><b style="background-color: white; color: #222222;"> x <span style="background-color: white;">16 </span><sup style="background-color: white;">-1</sup></b><span style="background-color: white; color: #222222;"> + </span><b style="background-color: white;"><span style="color: red;">F</span><span style="color: #222222;"> x </span><span style="background-color: white; color: #222222;">16 </span><sup style="background-color: white; color: #222222;">-2</sup></b><span style="background-color: white; color: #222222;"> + </span><b style="background-color: white; color: #222222;">9 x <span style="background-color: white;">16 </span><sup style="background-color: white;">-3</sup></b><span style="background-color: white; color: #222222;"><b> </b></span></div>
<div style="color: #222222;">
<span style="background-color: white;"> ↑ ↑</span><br />
<span style="background-color: white;"> MSD LSD</span><br />
<br /></div>
<div>
<b style="background-color: white; color: #222222;">= 4</b><b style="background-color: white; color: #222222;"> x 256<sup style="background-color: white;"> </sup>+ 1 x 16<sup style="background-color: white;"> </sup>+ </b><b style="background-color: white;"><span style="color: red;">10</span></b><b style="background-color: white; color: #222222;"> x 1<sup style="background-color: white;"> </sup>. </b><b style="background-color: white;"><span style="color: red;">14</span></b><b style="background-color: white; color: #222222;"> x ( 1 / 16 )</b><span style="background-color: white; color: #222222;"> + </span><b style="background-color: white;"><span style="color: red;">15</span><span style="color: #222222;"> x ( 1 / 256 ) </span></b><span style="background-color: white; color: #222222;">+ </span><b style="background-color: white; color: #222222;">9 x ( 1 / 4096 ) </b><span style="background-color: white; color: #222222;"> </span></div>
<div style="color: #222222;">
<b><br />
</b><br />
<b style="background-color: white;">= 1024</b><b style="background-color: white;"><sup style="background-color: white;"> </sup>+ 16<sup style="background-color: white;"> </sup>+ 10 <sup style="background-color: white;"> </sup>. ( 0 . 875 ) </b><span style="background-color: white;"> + <b>(</b> </span><b style="background-color: white;">0 . 005859 ) </b><span style="background-color: white;">+ <b>(</b> </span><b style="background-color: white;">0 . 00219 )</b></div>
<div style="color: #222222;">
<b><br />
</b></div>
<div>
<b><span style="color: #222222;">= </span><span style="color: #38761d;"> ( 1050</span></b><b><span style="color: #38761d;"> <sup style="background-color: white;"> </sup>. 883049 )<sub>16</sub></span></b><b style="color: #222222;"> </b></div>
<div style="color: #222222;">
<b><br />
</b></div>
</div>
</div>
</div>
<div>
<br /></div>
<div>
<b>NOTE:</b></div>
<div>
<b>Here the alphabets in the hexadecimal number system have the following decimal values and we use these values for representing the hexadecimal numbers in the decimal number system</b></div>
<div>
<span style="color: red;"><b><br />
</b></span><br />
<b style="color: red;">A </b><span style="color: red;">→</span><span style="color: red;"> </span><b style="color: red;">10</b><br />
<b style="color: red;"><br />
</b><br />
<b style="color: red;">B </b><span style="color: red;">→</span><span style="color: red;"> </span><b style="color: red;">11</b> <br />
<b style="color: red;"><br />
</b><br />
<b style="color: red;">C </b><span style="color: red;">→ </span><b style="color: red;">12</b><br />
<b style="color: red;"><br />
</b><br />
<b style="color: red;">D </b><span style="color: red;">→ </span><b style="color: red;">13</b><br />
<b style="color: red;"><br />
</b><br />
<b style="color: red;">E </b><span style="color: red;">→ </span><b style="color: red;">14</b><br />
<b style="color: red;"><br />
</b><br />
<b style="color: red;">F </b><span style="color: red;">→ </span><b style="color: red;">15</b><br />
<br class="Apple-interchange-newline" /></div>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-59123825979107963292012-01-26T05:34:00.000-08:002012-01-26T05:35:29.120-08:00Hexadecimal number representation<div dir="ltr" style="text-align: left;" trbidi="on">Representation of a number in the hexadecimal number system involves the same sequence of steps that we have used in representation of numbers in decimal, binary and hexadecimal number system, the main difference here is the weights used in hexadecimal number system are powers of 8 and the values that are assigned to these positional hexadecimal weights range from 0 to F. In this system it is not permitted to use the digits beyond 9 and alphabets beyond F.<br />
<br />
<u style="font-weight: bold;">nNote:</u> In hexadecimal number system 10 is not equal to ten but its equal to 16 in decimal.<br />
<br />
Let us take a simple example <b>8226</b> in <b>decimal number</b> system and (<b> 2022 </b>) its equivalent number in the hexadecimal number system, we will not worry much about how we obtained hexadecimal equivalent of the decimal number at this point.<br />
<br />
<br />
<u style="font-weight: bold;">Step 1:</u> <b>( 2 0 2 2 )<sub>16</sub></b><br />
Here subscript <b>16</b> indicates the number is in hexadecimal number system<br />
<br />
We also represent numbers in the hexadecimal number system as ( <b>2 0 2 2</b> )<b><sub>H</sub></b><br />
Here <b>H </b>means hexadecimal number system.<br />
<br />
We will now write down the weights in the form of table without assigning the values as shown below<br />
<br />
<br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> <b>16</b></span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">3</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1 </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← Weights in hexadecimal number system</b><br />
<table border="1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px; text-align: left;"><tbody>
<tr><td> </td><td> </td><td> </td><td> </td></tr>
</tbody></table><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">MSD LSD</span><br />
<div><br />
</div><div><br />
</div><div><u style="font-weight: bold;">Step 2 :</u> The values for the hexadecimal weights are assigned beginning from LSD to MSD, the right most digit in the given example is LSD and the left most digit is MSD as done below :</div><div><br />
</div><div><br />
</div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> </span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">3</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 16</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1 </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← Weights in hexadecimal number system</b><br />
<table border="1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px; text-align: left;"><tbody>
<tr><td> 2 </td><td> 0 </td><td> 2 </td><td> 2 </td></tr>
</tbody></table><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">MSD LSD</span></div><div><br />
</div><div><u style="font-weight: bold;">Step 3:</u> Determine the weight-value product by multiplying the values and the corresponding weights according to the position as shown below </div><div><br />
</div><div>Beginning from LSD to MSD</div><div><br />
</div><div>2 x <b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0 </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">←</span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> LSD </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← (1)</b></div><div>2 x <b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1 </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← (2)</b></div><div>0 x <b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2 </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← (3)</b></div><div>2 x <b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">3 </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← MSD </b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← (4)</b></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><br />
</b></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><br />
</b></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><br />
</b></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><u style="font-weight: bold;">Step 4:</u> Sum the individual products <b>(1), </b></span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">(2), (3), (4) </b><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">from step 3 as illustrated below</span></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><br />
</span></div><div><b> 2 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">3 </sup>+ 0 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">2 </sup>+ 2 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">1 </sup>+ 2 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">0</sup></b><br />
<b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</sup></b></div><div><b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup></b><b>= 2 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">3 </sup>+ 0 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">2 </sup>+ 2 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">1 </sup>+ 2 x <span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">16 </span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">0</sup></b></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> MSD LSD</span><br />
<br />
</div><div><b>= 2 x <span style="line-height: 18px;">4096</span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup>+ 0 x 256<sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup>+ 2 x <span style="line-height: 18px;">16</span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup>+ 2 x <span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;">1</span></span></b></div><div><b><br />
</b><br />
<b>= 8192<sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup>+ 0<sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> </sup>+ <span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">32 </span>+ 2</b></div><div><b><br />
</b><br />
<b>= <span style="color: #6aa84f;"> ( 8226 )<sub>16</sub></span></b><b><span style="color: #6aa84f;"> </span></b></div><div><br />
</div><div><br class="Apple-interchange-newline" /></div></div>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-83862779261736877842012-01-25T04:45:00.000-08:002012-01-25T04:45:03.552-08:00Hexadecimal number system.<div dir="ltr" style="text-align: left;" trbidi="on">So far we have seen three number systems and we are familiar with the number systems. Now we will be discussing another number system that is more commonly used in the electronic industry, the hexadecimal number system from the name by this you would have guessed it. Yes, this number system uses 16 symbols or digits.<br />
<br />
The radix or the base of the hexadecimal number system is 16 since it involves 16 symbols in counting as well as various arithmetic and logical operations.<br />
<br />
The hexadecimal number system starts from 0 to F ( i.e. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F).<br />
<br />
It would take sometime for you to get adjusted to this number system, which uses a both digits and alphabets.<br />
<br />
The positional weights in the hexadecimal number system are all powers of 16.<br />
<br />
<br />
The general format of hexadecimal number system is illustrated below.<br />
<br />
<br />
<b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br class="Apple-interchange-newline" /> 16<sup>4</sup> 16<sup>3</sup> 16<sup>2</sup> 16<sup>1</sup> 16<sup>0</sup> 16<sup>-1</sup> 16<sup>-2</sup> 16<sup>-3</sup> 16<sup>-4 </sup>←</b><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><b> Hexadecimal Weights</b></span><br />
<table border="1" bordercolor="dfdfdf" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px; text-align: left;"><tbody>
<tr><td><b> S<sub>4 </sub> </b></td><td><b> S<sub>3 </sub> </b></td><td><b> S<sub>2 </sub> </b></td><td><b> S<sub>1 </sub> </b></td><td><b> S<sub>0 </sub> </b></td><td><b> . </b></td><td><b> S<sub>-1 </sub> </b></td><td><b> S<sub>-2 </sub> </b></td><td><b> S<sub>-3 </sub> </b></td><td><b> S<sub>-4 </sub> </b></td></tr>
</tbody></table><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> </b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">↑</b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> ↑ </b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">↑</b><br />
<b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">MSD Hexadecimal point LSD</b><br />
<b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><br />
</b><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: x-small;"><span style="line-height: 18px;"><b><br />
</b></span></span><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;">where </span></span><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;"> <b>MSD i the most significant digit</b></span></span><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;"><b> LSD is the least significant digit</b></span></span><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;"><b><br />
</b></span></span><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;"><b> </b></span></span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">S<sub>1</sub></b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ,S<sub>2</sub></b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ,S<sub>3 ....</sub></b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">Sn</b><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><sub> </sub></b><b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">are values assigned.</b><br />
<b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"><br />
</b><br />
<span style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="line-height: 18px;"><b><br />
</b></span></span><br />
</div>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-52925669015533924182012-01-23T07:30:00.001-08:002020-11-22T12:32:46.090-08:00Convert octal fraction to decimal fraction<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;">Solved examples of octal fractions to decimal fraction conversion</span><br />
<div dir="ltr" style="background-color: white; color: #222222; line-height: 18px;" trbidi="on">
<div dir="ltr" trbidi="on">
<br />
<u style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">Problem 1:</u><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> Convert ( 2 1 . 2 1 )</span><sub style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">8</sub><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;">= ( ? )</span><sub style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">10</sub><br />
<sub style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</sub><br />
<span style="font-family: inherit;"><sub>= <span style="font-size: small;"> 2 1 <b>.</b> 2 1</span></sub><br />
<span style="background-color: white;"> ↑</span><span style="background-color: white;"> ↑</span><br />
<span style="vertical-align: sub;">MSD LSD</span></span></div>
<br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">= 2 x 8<sup>1</sup> + 1 x 8<sup>0</sup> . 2 x 8<sup>-1</sup></b> <b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">+ 1 x 8<sup>-2</sup></b><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> </span><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> </span><br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><sup><br />
</sup></b><br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">= 2 x 8 + 1 x 1 . 2 x ( 1 / 8 )</b><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> </span><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">+ 1 x ( 1 / 64 )</b><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> </span><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b><br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b><br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">= 16 + 1 . ( 0. 2 5 )</b><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> </span><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">+ </b><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"> ( 0 . 0 1 5 6 2 5 )</b><span style="font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif;"> </span><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b><br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><br />
</b><br />
<b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;">= 17 + 0. 265625</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div dir="ltr" trbidi="on">
<b>= 17 . </b><b style="background-color: white;">265625</b></div>
<br />
<br />
<b>Therefore <span style="color: #38761d;"> ( 2 1 . 2 1 )<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 1 7 . 2 6 5 6 2 5 )<sub>10</sub></span></b></div>
<br />
<hr style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" />
<br />
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div dir="ltr" trbidi="on">
<br />
<u style="font-weight: bold;">Problem 2:</u> Convert ( 0.357 )<sub>8</sub>= ( ? )<sub>10</sub><br />
<sub><br />
</sub><br />
<sub><span style="font-size: small;">= 0 <b>.</b> 3 5 7</span></sub><br />
<span style="background-color: white;"> ↑</span><span style="background-color: white;"> ↑</span><br />
<span style="vertical-align: sub;">MSD LSD</span></div>
<br />
<b>= 0 x 8<sup>0</sup> . 3 x 8<sup>-1</sup></b> <b>+ 5 x 8<sup>-2</sup></b> <b>+ 7 x 8<sup>-3</sup></b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><sup><br />
</sup></b><br />
<b>= 0 x 1 . 3 x ( 1 / 8 )</b> <b>+ 5 x ( 1 / 64 )</b> <b>+ 7 x ( 1 / 512 )</b> </div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<b>= 0 . (0. 375)</b> <b>+ (0 . 0 7 8 1 2 5 ) </b> <b>+ </b><b>( 0.013671875 )</b> </div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<b>= 0 . ( 0 . 466796875 )</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<div dir="ltr" trbidi="on">
<b>= </b><b style="background-color: white;">0 . 466796875</b></div>
<br />
<br />
<b>Therefore <span style="color: #38761d;"> ( 0 . 3 5 7)<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 0 . 466796875 )<sub>10</sub></span></b></div>
<br />
<hr style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" />
<br />
<br />
<div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<div dir="ltr" trbidi="on">
<u style="font-weight: bold;">Problem 3:</u> Convert ( 100.01 )<sub>8</sub>= ( ? )<sub>10</sub><br />
<sub><br />
</sub><br />
<span style="font-size: small;"><sub><span style="font-size: small;">= 1 0 0 <b>.</b> 0 1</span></sub></span><span style="background-color: white;"> </span><br />
<b style="background-color: white;"><span style="background-color: white; font-weight: normal;"> ↑</span><span style="background-color: white; font-weight: normal;"> ↑</span></b></div>
<div dir="ltr" style="background-color: white;" trbidi="on">
<b><span style="font-weight: normal; vertical-align: sub;"> MSD LSD</span></b><br />
<b><span style="font-weight: normal; vertical-align: sub;"><br />
</span></b></div>
<b>= 1</b><b> x 8<sup>2 </sup></b><b>+ 0 x 8<sup>1 </sup></b><b>+ 0 x 8<sup>0</sup></b><b> . 0 x 8<sup>-1 </sup></b><b>+ 1 x 8<sup>-2</sup></b> </div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><sup><br />
</sup></b><br />
<b>= 1</b><b> x 64<sup> </sup></b><b>+ 0 x 8<sup> </sup></b><b>+ 0 x 1</b><b> . 0 x ( 1 / 8 )<sup> </sup></b><b>+ 1 x ( 1 / 64 )</b><br />
<b><br />
</b><br />
<b>= 64 + 0 </b><b>+ 0 </b><b> . ( 0 )<sup> </sup></b><b>+ </b><b> ( 0. 015625 )</b> <b><br />
</b><br />
<b><br />
</b><br />
<b>= 64</b><b><sup> </sup></b><b> </b><b> . </b> <b>( 0. 015625 )</b> </div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b></div>
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" trbidi="on">
<b><br />
</b><br />
<div dir="ltr" trbidi="on">
<b>= 64 . 015625</b></div>
<br />
<br />
<b>Therefore <span style="color: #38761d;"> ( 1 0 0 . 0 1 )<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 64 . 0 1 5 6 2 5 )<sub>10</sub></span></b></div>
<br />
<hr style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;" />
<br />
<span style="color: #990000;"><u><b>Related Posts</b></u></span><br />
<span style="color: #990000;"><br /></span>
<span style="color: #cc0000;"><a href="https://www.schoolelectronic.com/2012/01/fractions-in-octal-number-system.html">Step by step procedure to convert octal fraction to decimal fraction</a></span><br />
<div dir="ltr" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" trbidi="on">
<span style="color: #990000;"><br class="Apple-interchange-newline" /></span>
<br />
<div style="text-align: left;">
<span style="color: #990000;"><span style="font-size: small;"><a href="https://www.schoolelectronic.com/2013/11/Octal-to-binary-conversion-method-with-example.html">Octal to binary conversion procedure</a></span></span></div>
</div>
</div>
</div>
School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-61197999887155873862012-01-23T00:07:00.000-08:002012-01-27T04:44:13.307-08:00Convert octal to decimal number<div dir="ltr" style="text-align: left;" trbidi="on">Illustrated examples for converting octal numbers to equivalent decimal number.<br />
<div dir="ltr" trbidi="on"><div dir="ltr" trbidi="on"><div dir="ltr" trbidi="on"><br />
<u style="font-weight: bold;">Problem 1:</u> Convert ( 237 )<sub>8</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= 2 3 7</span></sub><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑</span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑</span><br />
<span style="font-size: x-small;">MSB</span> <span style="font-size: x-small;">LSB</span></div><br />
<b>= 2 x 8<sup>2</sup> + 3 x 8<sup>1</sup> + 7 x 8<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= 2 x 64 + 3 x 8 + 7 x 1</b><br />
<b><br />
</b><br />
<b>= 128 + 24 + 7</b><br />
<b><br />
</b><br />
<b>= 159</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( 2 3 7 )<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 1 5 9 )<sub>10</sub></span></b></div><br />
<hr /><br />
<div dir="ltr" trbidi="on"><u style="font-weight: bold;">Problem 2:</u> Convert ( 1000 )<sub>8</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= 1 0 0 0</span></sub><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑</span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑</span><br />
<span style="vertical-align: sub;"><span style="font-size: x-small;">MSB</span> <span style="font-size: x-small;"> LSB</span></span></div><br />
<b>= 1 x 8<sup>3</sup> + 0 x 8<sup>2</sup> + 0 x 8<sup>1</sup></b><b>+ 0 x 8<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= 1 x 512 + 0 x 64 + 0 x 8 </b><b>+ 0 x 1</b><br />
<b><br />
</b><br />
<b>= 512 + 0 + 0 </b><b>+ 0</b><br />
<b><br />
</b><br />
<b>= 512</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( 1 0 0 0 )<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 5 1 2 )<sub>10</sub></span></b><br />
<span style="color: #38761d; font-size: x-small;"><b><br />
</b></span><br />
<hr /><div dir="ltr" trbidi="on"><u style="font-weight: bold;"><br class="Apple-interchange-newline" />Problem 3:</u> Convert ( 7777 )<sub>8</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= 7 7 7 7 </span></sub><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑</span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> ↑</span><br />
<span style="vertical-align: sub;"><span style="font-size: x-small;">MSB</span> <span style="font-size: x-small;">LSB</span></span></div><br />
<b>= 7 x 8<sup>3</sup> + 7 x 8<sup>2</sup> + 7 x 8<sup>1</sup></b><b>+ 7 x 8<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= 7 x 512 + 7 x 64 + 7 x 8 </b><b>+ 7 x 1</b><br />
<b><br />
</b><br />
<b>= 3584 + 448 + 56 </b><b>+ 7</b><br />
<b><br />
</b><br />
<b>= 4095</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( 7 7 7 7 )<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 4 0 9 5 )<sub>10</sub></span></b><br />
<b><span style="color: #38761d;"><sub><br />
</sub></span></b><br />
<hr /><div dir="ltr" trbidi="on"><u style="font-weight: bold;"><br />
</u><br />
<u style="font-weight: bold;">Problem 4:</u> Convert ( 2 0 )<sub>2</sub>= ( ? )<sub>10</sub><br />
<sub><span style="font-size: small;"><br />
</span></sub><br />
<sub><span style="font-size: small;">= 2 0</span></sub><br />
<span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> </span></div><b>= 2 x 8<sup>1</sup></b><b>+ 0 x 8<sup>0</sup></b><br />
<b><sup><br />
</sup></b><br />
<b>= 2 x 8 </b><b>+ 0 x 1</b><br />
<b><br />
</b><br />
<b>= 16 + 0 </b><br />
<b><br />
</b><br />
<b>= 16</b><br />
<b><br />
</b><br />
<b>Therefore <span style="color: #38761d;"> ( 2 0 )<sub>8</sub></span></b><b><span style="color: #38761d;"> = ( 1 6 )<sub>10</sub></span></b><br />
<span style="color: #38761d; font-size: x-small;"><b><br />
</b></span></div></div>School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.comtag:blogger.com,1999:blog-5808856167298706053.post-86071430604536794762012-01-22T23:03:00.000-08:002019-08-03T15:33:53.159-07:00Fractions in octal number system<div dir="ltr" style="text-align: left;" trbidi="on">
In this, We will discuss about how we represent fractional numbers in octal number system.<br />
<div>
The octal point plays the same role as that of decimal point in decimal number system and binary point in the binary number system i.e. it separates the integer binary bits and fractional bits.</div>
<div>
<br /></div>
<div>
The procedure is similar to the procedure we followed to represent decimal fraction and binary fractions.</div>
<div>
<br /></div>
<div>
Each step involved in representation of the fractions in the octal number system is illustrated below.</div>
<div>
<br /></div>
<div>
<br /></div>
<div>
Example 1:<b> (407.304)<sub>8</sub></b> is the octal equivalent of ( 2<b>63.3828125 )</b> in decimal number system.</div>
<div>
<u style="font-weight: bold;"><br />
</u></div>
<div>
<u style="font-weight: bold;">Step 1:</u></div>
<div>
<br /></div>
<div>
Write down the sequence of octal weights based on the number of digits in the given octal number separated by the octal point as shown below</div>
<div>
<br />
<br />
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;"> </span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 8</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 8</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0 </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-1</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-2</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-3</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← Weights</b><br />
<table border="1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px; text-align: left;"><tbody>
<tr><td> </td><td> </td><td> </td><td> <b>.</b> </td><td> </td><td> </td><td> </td></tr>
</tbody></table>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;">MSD LSD</span><br />
<br />
<u style="font-weight: bold;">Step 2:</u> Assign the values for the weights starting from LSD till the octal point and again starting from the octal point assign the integer values up to the MSD as done below.<br />
<br />
<br />
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;"><br class="Apple-interchange-newline" /> </span><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">2</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 8</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">1</sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;"> 8</b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">0 </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-1</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-2</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">8 </b><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;">-3</sup><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-weight: bold;"> </sup><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">← Weights</b><br />
<table border="1" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px; text-align: left;"><tbody>
<tr><td> 4 </td><td> 0 </td><td> 7 </td><td> <b>.</b> </td><td> 3 </td><td> 0 </td><td> 4 </td></tr>
</tbody></table>
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;"> ↑ ↑</span><br />
<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; line-height: 18px;">MSB LSB</span></div>
<div>
<br />
<br />
<u style="font-weight: bold;">Step 3:</u> Compute the product of individual octal digits and its associated weights to get the products which looks like the following<br />
<br />
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
3 x <b style="background-color: white;">8 </b><sup style="background-color: white; font-weight: bold;">-1 </sup><sup style="background-color: white;"> </sup><span style="background-color: white;">←</span><b style="background-color: white;"> LSD </b><sup style="background-color: white; font-weight: bold;"> </sup></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
0 x <b style="background-color: white;">8 </b><sup style="background-color: white; font-weight: bold;">-2 </sup></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
4 x <b style="background-color: white;">8 </b><sup style="background-color: white; font-weight: bold;">-3</sup></div>
<div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
<sup style="background-color: white; font-weight: bold;"><span style="font-size: small;"> . </span></sup></div>
<div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18px;">
<div style="color: #222222;">
7 x <b style="background-color: white;">8 </b><sup style="background-color: white; font-weight: bold;">0 </sup></div>
<div style="color: #222222;">
0 x <b style="background-color: white;">8 </b><sup style="background-color: white; font-weight: bold;">1</sup></div>
<div style="color: #222222;">
4 x <b style="background-color: white;">8 </b><sup style="background-color: white; font-weight: bold;">2 </sup><b style="background-color: white;">← MSD </b></div>
<div style="color: #222222;">
<b style="background-color: white;"><br />
</b></div>
<div style="color: #222222;">
<b style="background-color: white;"><br />
</b></div>
<div style="color: #222222;">
<b style="background-color: white;"><u>Step 4:</u> </b><span style="background-color: white;">Add the individual products separated by the octal point as illustrated below</span></div>
<div style="color: #222222;">
<span style="background-color: white;"><br />
</span></div>
<div>
<div style="color: #222222;">
<b> 4 x <span style="background-color: white;">8 </span><sup style="background-color: white;">2 </sup>+ 0 x 8<span style="background-color: white;"> </span><sup style="background-color: white;">1 </sup>+ 7 x 8<span style="background-color: white;"> </span><sup style="background-color: white;">0 </sup>. 3 x <span style="background-color: white;">8 </span><sup style="background-color: white;">-1</sup></b> + <b>0 x <span style="background-color: white;">8 </span><sup style="background-color: white;">-2</sup></b> + <b>4 x <span style="background-color: white;">8 </span><sup style="background-color: white;">-3</sup></b><br />
<b><sup style="background-color: white;"><br />
</sup></b></div>
<div style="color: #222222;">
<b style="background-color: white;"><sup style="background-color: white;"> </sup></b><b style="background-color: white;">= 4</b><b style="background-color: white;"> x <span style="background-color: white;">8 </span><sup style="background-color: white;">2 </sup>+ 0 x <span style="background-color: white;">8 </span><sup style="background-color: white;">1 </sup>+ 7 x <span style="background-color: white;">8 </span><sup style="background-color: white;">0 </sup>. 3 x <span style="background-color: white;">8 </span><sup style="background-color: white;">-1</sup></b><span style="background-color: white;"> + </span><b style="background-color: white;">0 x <span style="background-color: white;">8 </span><sup style="background-color: white;">-2</sup></b><span style="background-color: white;"> + </span><b style="background-color: white;">4 x <span style="background-color: white;">8 </span><sup style="background-color: white;">-3</sup></b><span style="background-color: white;"> </span></div>
<div style="color: #222222;">
<span style="background-color: white;"> ↑ ↑</span><br />
<span style="background-color: white;"> MSD LSD</span><br />
<br /></div>
<div style="color: #222222;">
<b style="background-color: white;">= 4</b><b style="background-color: white;"> x 64<sup style="background-color: white;"> </sup>+ 0 x <span style="background-color: white;">8</span><sup style="background-color: white;"> </sup>+ 7 x 1<sup style="background-color: white;"> </sup>. 3 x ( 1 / 8 )</b><span style="background-color: white;"> + </span><b style="background-color: white;">0 x ( 1 / 64 ) </b><span style="background-color: white;">+ </span><b style="background-color: white;">4 x ( 1 / 512 ) </b><span style="background-color: white;"> </span></div>
<div style="color: #222222;">
<b><br />
</b><br />
<b style="background-color: white;">= </b><b style="background-color: white;">256<sup style="background-color: white;"> </sup>+ 0<sup style="background-color: white;"> </sup>+ 7 <sup style="background-color: white;"> </sup>. ( 0 . 375 ) </b><span style="background-color: white;"> + <b>(</b> </span><b style="background-color: white;">0 ) </b><span style="background-color: white;">+ <b>(</b> </span><b style="background-color: white;">0 . 0078125 )</b></div>
<div style="color: #222222;">
<b><br />
</b></div>
<div>
<b><span style="color: #222222;">= </span><span style="color: #38761d;"> ( 263</span></b><b><span style="color: #38761d;"> <sup style="background-color: white;"> </sup>. 3828125 )<sub>10</sub></span></b><b style="color: #222222;"> </b></div>
<div style="color: #222222;">
<b><br />
</b></div>
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<a href="https://www.schoolelectronic.com/2012/01/convert-octal-fraction-to-decimal.html">Illustrated Examples</a></div>
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School electronicshttp://www.blogger.com/profile/17328324384328603109noreply@blogger.com