The octal numeral system is the base-8 number system, and uses the digits 0–7. According to Donald Knuth's The Art of Computer Programming, it was invented by King Charles XII of Sweden.

Octal numerals can be made from binary numerals by grouping consecutive digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which groups into 1 001 010 — so the octal representation is 112.

Octal is sometimes used in computing instead of hexadecimal, perhaps most often in conjunction with file permissions under UNIX systems (see Chmod). It has the advantage of not requiring any extra symbols as digits (the hexadecimal system is base-16 and therefore needs six additional symbols beyond 0–9). However it has a disadvantage in that while two hex digits make a byte, three octal digits would be required, with the most significant octal digit inelegantly representing only two binary digits (and in a series the same octal digit would represent one binary digit from the next byte).

Octal counting may have been used in the past instead of decimal counting, by counting either the gaps between fingers or the non-thumb fingers. This may explain why the Latin for nine novem is so much like the Latin for new novus. It may have meant new number.

See also

• Computer numbering formats