Tuesday, September 7, 2010

Octal

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which can be grouped into (00)1 001 010 — so the octal representation is 112.
In decimal systems each decimal place is a base of 10. For example:
\mathbf{74}_{10} = \mathbf{7} \times 10^1 + \mathbf{4} \times  10^0
In octal numerals each place is a power with base 8. For example:
\mathbf{112}_8 = \mathbf{1} \times  8^2 + \mathbf{1} \times  8^1 + \mathbf{2} \times  8^0
By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal.
Octal is sometimes used in computing instead of hexadecimal.

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