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 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.

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

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

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

Related pages

• Binary numeral system
• Hexadecimal numeral system
• Decimal numeral system

Other websites

• Online Converter Archived 2007-01-04 at the Wayback Machine for Decimal/Octal Numerals (JavaScript, GPL)