Octal Notation
Octal notation is a method of representing octal (base 8) numbers using the eight numerals 0-7. Octal notation uses positional notation and powers of 8 to express to express numbers in a manner similar to that of the familiar decimal system. In the decimal number system, the positions of the digits 0 through 9 determine their values. Consider the decimal number 375; the digits 5, 7, and 3 are understood to be multiplied by increasing powers of 10.
Explicitly, 37510 = (3 x 102) + (7 x 101) + (5 x 100) = 300 + 70 + 5. Octal 567 is the same number as decimal 375: 5678 = (5 x 82) + (6 x 81) + (7 x 80) = 5x64 + 6x 8 + 7 x 1 = 320 + 48 + 7 = 375.
Each octal digit is the equivalent value of three binary digits. For example, octal 235 can be converted to a binary number by transforming each of its three digits to a binary triple. The leading 2 is 010 in binary notation, that is, (0 x 22) + (1 x 21) + (0 x 20) = 0 + 2 + 0 = 2; the 3 is 011 by (0 x 22) + (1 x 21) + (1 x 20) = 0 + 2 + 1 = 3; and the 5, similarly, is equivalent to binary101. Thus octal 235 equals binary 010010101. Hexadecimal notation is more commonly used in contemporary computer work than octal notation.
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