- 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 8^{0}, the next representing 8^{1}, then 8^{2}, 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 )**_{8 }= ( ? )_{10 }=[ 5× 8^{2 }] + [ 6 × 8^{1 }]+ [ 7 × 8^{0 }]

=[ 320 ]+[ 48 ]+[ 7 ]

=( 3 7 5 )_{10}**Example 2:**

**( 0000 )**_{8 }= ( ? )_{10 }=[ 0 × 8^{3 }] + [ 0 ×82^{2 }] + [ 0 × 8^{1 }] + [ 0 × 8^{0}]

=[ 0 ]+[ 0 ]+[ 0 ]+[ 0 ]

=( 0 )_{10}**Example 3:**

**( 0.5067)**_{8 }= ( ? )_{10 }=[ 0 × 8^{0 }] +[ 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 × 8^{2}] + [ 3 × 8^{1}] + [ 1 × 8^{0}] + [ 5 × 8^{-1}] +[ 6 × 8^{-2}]

= [ 448 ] + [ 24 ] + [ 1 ] + [ 0.625 ] + [ 0.09375 ]

= ( 473.71875 )_{10}**Example 5:**

**( 777 )**_{8}= ( ? )_{10}

= [ 7× 8^{2 }] +[ 7 × 8^{1 }]+ [ 7 × 8^{0 }]

=[ 448 ]+[ 56 ]+[ 7 ]

=( 511 )_{10}