# Octal to decimal number system

• Any octal number can be converted to its decimal equivalent using the weight assigned to each bit position .Octal number system has base 8.
For example,
Suppose we have a number (761.15)8 then weight assigned to each bit is ,
shown below : To the left of radix point power of eight increases,while to the right of radix point power of eight decreases.

• In the octal system,
Going to the left of  radix point each digit represents an increasing power of 8, with the right most digit representing 80, the next representing 81, then 82, and so on.
And going to the right of radix point,each digit represent an decreasing power of 8 , with left most digit representing 8-1,the next representing 8-2,then 8-3 ,then 8-4 and so on.
The equivalent decimal representation of a octal number is the sum of the powers of  8 ,which each digit represents.

The octal number is converted to decimal number as follows:
• Example 1:
( 567 )= (   ?  )10
=[ 5× 8] + [ 6 × 8]+ [ 7 × 8]
=[ 320 ]+[ 48 ]+[ 7 ]

=( 3 7 5  )10
• Example 2:
( 0000 )= (   ?  )10
=[ 0 ×  83 ] + [ 0  ×82] + [ 0  × 8]  + [ 0  × 80]
=[ 0 ]+[ 0 ]+[ 0 ]+[ 0 ]

=( 0 )10
• Example 3:
( 0.5067)= (  ?  )10
=[ 0 × 8] +[ 5 × 8-1 ] + [ 0 × 8-2 ] + [ 6 × 8-3 ] + [ 7 × 8-4  ]
=[ 0 ]+[ 0.625 ]+[ 0 ]+[ 0.01171875 ]+[ 0.00170898 ]
=( 0.63842773 )10
• Example 4:
(731.56)8 = (  ?  )10
= [  7  × 82 ] + [  3  × 81 ] + [  1  × 80 ] + [  5  × 8-1 ] +[  6  × 8-2 ]
= [ 448 ] + [ 24 ] + [ 1 ] + [ 0.625 ] + [ 0.09375 ]
= ( 473.71875 )10
• Example 5:
( 777 )8 = (   ?   )10
= [ 7× 8] +[ 7 × 8]+ [ 7 × 8]
=[ 448 ]+[ 56 ]+[ 7 ]
=( 511 )10