Computer programmers often use octal numerals instead of binary numerals because it is easy to convert from binary to octal directly. The table below shows this conversion.

Octal Binary Equivalence

Octal Binary

$0000$

$1001$

$2010$

$3011$

$4100$

$5101$

$6110$

$7111$

A binary number $1101110111$ is separated into three$-$digit groupings by starting at the right end of the number and supplying leading zeros at the left if necessary: $001101110111.$ The binary groups are then replaced by their octal equivalents:

$001$two $=1$eight $101$two $=5$eight

$110$two $=6$eight $111$two $=7$eight

and the binary number is converted to its octal equivalent: $1567.$ Conversely, an octal number can be expanded to a binary number using the same table of equivalents:

$5307$eight $=101011000111$two.