Octal

The octal numeral system is a base 8 numeral system. It uses the numerals 0 through 7. The system is similar to binary (base 2) and hexadecimal (base 16). Octal numerals are written using the letter o before the numeral, for example, o04 or o1242. Octal numbers are also sometimes written with a small 8 to the lower right, as in 12428.

At one time, the octal system was used mainly for work with computers. It provided an easier way to work with binary numbers. As computers changed from using 24-bit systems to 32- and 64-bit systems, hexadecimal replaced octal for most uses. Certain groups, for example, Native Americans using the Yuki language in California and the Pamean languages[1] in Mexico, also use an octal numbering system. They do this because when they count, they use the spaces between their fingers instead of counting the actual fingers.

Octal and binary

The octal numeral system uses a "three-bit" binary coding. Each digit in an octal numeral is the same as three digits in a binary numeral. The grouping of the binary digits is done from right to left. The first three binary digits from the right are grouped into the last part of the octal numeral, then the next three digits form the next to the last part of the numeral.

OctalBinary
1001
2010
3011
4100
5101
6110
7111
10001 000
OctalBinary
11001 001
12001 010
36011 110
45100 101
53101 011
64110 100
100001 000 000
357011 101 111
BinaryGroupingsOctal
110113
01011101011127
101000110101000110506
010110101010010110101011325

Octal and decimal

In the decimal system (base 10), each digit in octal is equal to that digit multiplied by the exponent of 8 that is equal to its location minus one.

 Location
654321
Value 32768 (85)4096 (84)512 (83)64 (82)8(81)1 (80)

Example: o3425 to decimal

 
OctalDecimal
o3425=( 5 × 1 )+( 2 × 8)+( 4 × 64 )+( 3 × 512)
=5+16+256+1536
o3425=1813

Octal and hexadecimal

Octal is similar to hexadecimal because they are both easily converted to binary. Where octal is equal to three-digit binary, hexadecimal is equal to four-digit binary. Where octal numerals start with the letter "o", hexadecimal numerals end with the letter "h". The easiest way to convert from one to the other is to convert to binary and then to the other system.

OctalBinaryHexadecimal
three digitfour digit
o4100010004h
o1500110111010Dh
o30601100011011000110C6h
o54253101100010101011010110001010101158ABh

References
  1. Avelino, Heriberto (2006), "The typology of Pame number systems and the limits of Mesoamerica as a linguistic area" (PDF), Linguistic Typology, 10: 41–60, doi:10.1515/LINGTY.2006.002, S2CID 20412558

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