It is seen that the length of binary numbers can become quite long and cumbersome to use. Octal system (base 8) is thus often used to convert binary numbers to a form requiring lesser number of digits. The octal system uses the eight symbols 0, 1, 2, ……… 7. As its radix 8 is a power of 2, it is fairly simple to convert binary to octal and vice-versa.
To convert a binary number into an octal number, we will group together successive three bits of the binary number starting with its least significant bit (i.e., the right-most). These three bit groups are then replaced by their octal equivalents. This mechanism works because all the digits in octal system, namely 0, 1, 2,……………7, may be represented by three bit groups. The table below illustrates this.
Octal Binary Octal Binary Octal Binary
0 000 3 011 6 110
1 001 4 100 7 111
2 010 5 101
Example : Binary numbers 001 100 111 001
Octal equivalent 1 4 7 1
Decimal equivalent 1 x 83
+ 4 x 82
+ 7 x 81
+ 1 x 8
0
= 512 + 256 + 56 + 1
= 825