Number system conversion

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.
     In the following posts we will discuss basic conversion techniques to convert any given number from one number system to another.

At this point you would ask me "hey why do we need to do this number conversion stuff? ".
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 example.

You are providing your mobile number to one your classmate for instance this is your mobile number (123)-456-0123 in the decimal number system and you decide to give it in the binary format as (1111011)-111001000-1111011.
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).

From the above example we can clearly make out when we require decimal and when we require binary number sytem.

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.
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.

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

  1. Decimal number system to binary number system
  2. Decimal number system to octal number system
  3. Decimal number system to hexadecimal number system
  4. Binary number system to decimal number system
  5. Octal number system to decimal number system
  6. Hexadecimal number system to decimal number system
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