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# Octal numeral system

The octal numeral system is a place-value numeral system based on the powers of 8, sometimes used as a shorthand for the binary numeral system.

For example, 11001001 is 311:

 ${\displaystyle 2^{7}}$ ${\displaystyle 2^{6}}$ ${\displaystyle 2^{5}}$ ${\displaystyle 2^{4}}$ ${\displaystyle 2^{3}}$ ${\displaystyle 2^{2}}$ ${\displaystyle 2^{1}}$ ${\displaystyle 2^{0}}$ 128s 64s 32s 16s 8s 4s 2s 1s 1 1 0 0 1 0 0 1 3 1 1 ${\displaystyle 8^{2}}$ ${\displaystyle 8^{1}}$ ${\displaystyle 8^{0}}$