Octal
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 3s (from 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. It has the advantage of not requiring any extra symbols as digits.
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.
Octal is as good as binary and hexadecimal for fractions, since the only prime factors for their bases are 2.
Fractions
| Decimal | Octal | Octal expansion |
|---|---|---|
| 1/2 | 1/2 | 0.4 |
| 1/3 | 1/3 | 0.25252525 recurring |
| 1/4 | 1/4 | 0.2 |
| 1/5 | 1/5 | 0.14631463 recurring |
| 1/6 | 1/6 | 0.125252525 recurring |
| 1/7 | 1/7 | 0.11111111 recurring |
| 1/8 | 1/10 | 0.1 |
| 1/9 | 1/11 | 0.07070707 recurring |
| 1/10 | 1/12 | 0.063146314 recurring |
See also: computer numbering formats