numeral system with eight as its base From Wikipedia, the free encyclopedia
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 1242_{8}.
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 24bit systems to 32 and 64bit 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.
The octal numeral system uses a "threebit" 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.



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 (8^{5})  4096 (8^{4})  512 (8^{3})  64 (8^{2})  8(8^{1})  1 (8^{0}) 
Example: o3425 to decimal

Octal is similar to hexadecimal because they are both easily converted to binary. Where octal is equal to threedigit binary, hexadecimal is equal to fourdigit 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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