# Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which can be grouped into (00)1 001 010 – so the octal representation is 112.

In the decimal system each decimal place is a power of ten. For example:

In the octal system each place is a power of eight. For example:

By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal.

### Other articles related to "octal":

Particular Octal Games - Nim
... The octal code for Nim is 0.333…, appearing in the published literature as , to signify the repeating part as in a repeating decimal ... that the repeating part does not play the same role as in octal fractions, in that the games and are not identical, despite their equality as octal fractions ...
Conversion Between Bases - Hexadecimal To Octal Conversion
... Hexadecimal to octal conversion proceeds by first converting the hexadecimal digits to 4-bit binary values, then regrouping the binary bits into 3-bit octal digits. 3FA516 To binary 3 F A 0101 ... then to octal 5 ... Therefore, 3FA516 = 376458 ...
Tube Socket - Octal
... base for their new metal envelope tubes, which they called an octal base ... Octal bases, as defined in IEC publication 67, diagram IEC 67-I-5a, have a 45 degree angle between pins, which form a 17.45 mm (11/16 inch) diameter circle around a 7.82 mm (5/16 inch) diameter keyed post (sometimes ... Octal sockets were designed to accept octal tubes, the rib in the keyed post fitting an indexing slot in the socket so the tube could only be ...
Binario - Conversion To and From Other Numeral Systems - Octal
... Binary is also easily converted to the octal numeral system, since octal uses a radix of 8, which is a power of two (namely, 23, so it takes exactly three binary digits to represent an octal digit) ... The correspondence between octal and binary numerals is the same as for the first eight digits of hexadecimal in the table above ... Binary 000 is equivalent to the octal digit 0, binary 111 is equivalent to octal 7, and so forth ...
Octal Game - Nim-sequence
... The analysis of an octal game then consists in finding the sequence of the nim-values for heaps of increasing size ... All finite octal games analyzed so far have shown a nim-sequence ultimately periodic, and whether all finite octal games are ultimately periodic is an open ...