Octal

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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.

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[change | change source]

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.

Octal Binary
1 001
2 010
3 011
4 100
5 101
6 110
7 111
10 001 000
Octal Binary
11 001 001
12 001 010
36 011 110
45 100 101
53 101 011
64 110 100
100 001 000 000
357 011 101 111
Binary Groupings Octal
11 011 3
010111 010 111 27
101000110 101 000 110 506
01011010101 001 011 010 101 1325

Octal and decimal[change | change source]

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
6 5 4 3 2 1
Value 32768 (85) 4096 (84) 512 (83) 64 (82) 8(81) 1 (80)

Example: o3425 to decimal

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

Octal and hexadecimal[change | change source]

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.

Octal Binary Hexadecimal
three digit four digit
o4 100 0100 04h
o15 001 101 1101 0Dh
o306 011 000 110 1100 0110 C6h
o54253 101 100 010 101 011 0101 1000 1010 1011 58ABh

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