Octal to Decimal – How to convert octal to Decimal

This post we will learn how to convert octal to decimal with Illustrated examples showing the conversion steps from a given octal number to an equivalent decimal number.

Octal to Decimal Converter

How to Convert Octal to Decimal

Step 1: We know that in the octal number system only 8 digits are used (from 0 to 7), so the first thing we do in converting a given number from octal to decimal is representing the octal number in powers of 8 or in other words we can say expressing the octal number with base as 8.

Step 2: In the second step, we evaluate all the power of 8 values such as 8⁰ is 1, 8¹ is 8 etc., and write down each octal digit multiplied with the evaluated power of 8 values.

Step 3: We then perform the multiplication of all the weights or octal digits with its respective power of 8 values.

Step 4: The final step in converting octal to decimal is adding all the individual values obtained after multiplying each octal digit with its power of 8 values. The sum total gives the decimal equivalent of the given octal number.

Let us see the above conversion with the help of an example for better understanding.

Octal to Decimal examples

Example 1: Convert ( 237 )₈ Octal to Decimal ( ? )₁₀

=  2  3  7
   ↑     ↑
  MSB   LSB

Step 1: Write down the given octal number and express it as power of 8 starting from right to left for integer values as shown below:

= 2 x 82 + 3 x 81 + 7 x 80

Step 2: Evaluate the Power of 8 values for each octal digit as show below

Where,

• 8⁰ = 1
• 8¹ = 8
• 8² = 64

= 2 x 64 + 3 x 8 +  7 x 1

Step 3: Multiply each power of 8 values with its respective octal digit as shown below:

Where,

• 7 x 1 = 7
• 3 x 8 = 24
• 2 x 64 = 128

Step 4: Add the values obtained after multiplication of each octal digit and the octal weights or power of 8 values.

= 128 + 24  + 7

The sum total gives the decimal equivalent[159] of the given octal number[237].

= 159

Therefore  ( 2 3 7 )8 =  ( 1 5 9 )10

Example 2: Convert ( 1000 )₈= ( ? )₁₀

=  1  0  0  0
   ↑        ↑
  MSB      LSB

= 1 x 83 + 0 x 82 + 0 x 81+ 0 x 80

= 1 x 512  + 0 x 64   + 0 x 8  + 0 x 1

= 512  +  0  +  0  +  0

= 512

Therefore  ( 1 0 0 0 )8 =  ( 5 1 2 )10

Example 3: Convert ( 7777 )₈ octal to decimal ( ? )₁₀

=  7  7  7  7 
   ↑        ↑
  MSB      LSB

= 7 x 83 + 7 x 82 + 7 x 81+ 7 x 80

= 7 x 512  + 7 x 64   + 7 x 8  + 7 x 1

=  3584 +  448  +  56  +  7

= 4095

Therefore  ( 7 7 7 7 )8 =  ( 4 0 9 5 )10

Example 4: Convert ( 2 0 )₈= ( ? )₁₀

=  2 0

= 2 x 81+ 0 x 80

= 2 x 8  + 0 x 1

= 16  +  0 

= 16

Therefore  ( 2 0 )8 =  ( 1 6 )10

Convert Fractional Octal to Decimal fraction

Converting octal to decimal with decimal point i.e when the given octal number has fractional part.

Solved examples of octal fractions to decimal fraction conversion

Example 1: Convert ( 2 1 . 2 1 )₈ Octal to decimal with Decimal point ( ? )₁₀

= 2 1 .  2  1
  ↑         ↑
 MSD       LSD

= 2 x 81 + 1 x 80 .  2 x 8-1 + 1 x 8-2  

= 2 x 8 + 1 x 1 .  2 x ( 1 / 8 ) + 1 x ( 1 / 64 )  

= 16 +  1  .  ( 0. 2 5 ) +  ( 0 . 0 1 5 6 2 5 ) 

= 17 +  0. 265625

 = 17 . 265625

Therefore  ( 2 1 . 2 1 )8 =  ( 1 7 . 2 6 5 6 2 5 )10

Example 2: Convert ( 0.357 )₈= ( ? )₁₀

=  0  . 3 5 7
   ↑        ↑
  MSD      LSD

=  0 x 80 .  3 x 8-1 + 5 x 8-2  + 7 x 8-3

=  0 x 1  .  3 x ( 1 / 8 ) + 5 x ( 1 / 64 )  + 7 x ( 1 / 512 )  

=  0  .  (0. 375) +  (0 . 0 7 8 1 2 5 )   +  ( 0.013671875 )

= 0  .  ( 0 . 466796875 )

= 0 . 466796875

 Therefore  ( 0 . 3 5 7)8 =  ( 0 . 466796875 )10

Example 3: Convert octal fraction ( 100.01 )₈ to Decimal ( ? )₁₀

=  1 0  0 . 0 1 
   ↑          ↑
  MSD        LSD

= 1 x 82 + 0 x 81 + 0 x 80 .  0 x 8-1 + 1 x 8-2 

= 1 x 64 + 0 x 8 + 0 x 1 .  0 x ( 1 / 8 ) + 1 x ( 1 / 64 )

= 64 + 0 + 0  .  ( 0 ) +  ( 0. 015625 )

= 64   .   ( 0. 015625 )    

= 64 . 015625

Therefore  ( 1 0 0 . 0 1 )8 =  ( 64 . 0 1 5 6 2 5 )10