Octal

Octal system (also known as base 8 or octonary), is a numeral system that uses the numerals 0 through 7. The system is similar to binary (base 2) and hexadecimal (base 16). Octal numerals are written using the number 0 before the numeral, for example, 004 or 01242. 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 system
the octal system has no letters of the alphabet
OctalBinary 1 00120103011410051016110711110001 000OctalBinary 11 001 00112001 01036011 11045100 10153101 01164110 100100001 000 000357011 101 111 BinaryGroupingsOctal11 0113010111    01011127101000110  101  000110506010110101010010110101011325

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.
 Location6 5 4 3 2 1Value32768 (85) 4096 (84) 512 (83) 64 (82) 8(81)1 (80)

Example: o3425 to decimal
 OctalDecimalo3425 = ( 5 × 1 ) + ( 2 × 8)+ ( 4 × 64 )+ ( 3 × 512)= 5 + 16+ 256+ 1536o3425=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 BinaryHexadecimalthree digitfour digito4100010004ho1500110111010Dho30601100011011000110C6ho54253101100010101011010110001010101158ABh

Related pages
 Binary numeral system
 Hexadecimal numeral system
 Decimal numeral system

 References 

 Other websites 
 Online Converter  for Decimal/Octal Numerals (JavaScript, GPL)

Category:Numbering systems