Octal

Octal, also known as "base-8," is a number system that uses eight digits (0 - 7) to represent any integer. Octal values are sometimes used to represent data in computer science since bytes contain eight bits. For example, the octal value "10" can represent 8 bits or 1 byte. "20" represents 2 bytes, 30 represents 3, etc. Octal values are also easily translatable from binary, which uses two digits, and hexadecimal, which uses 16 digits.

To convert an octal value to a standard decimal or "denary" value, multiply each digit by 8ⁿ, where n is the place of the digit, starting with 0, from right to left. Then add the results together. So 123 in octal can be converted to a decimal value as follows:

8⁰ x 3 + 8¹ x 2 + 8² x 1 = 3 + 16 + 64 = 83

The table below shows several equal values in octal, decimal, hexadecimal, and binary:

Binary to Octal Conversion

To convert a binary value to an octal value, separate the digits into groups of three, starting from right to left. Then mulitply each 1 or 0 by 2ⁿ, where n is the place of each digit, from right to left, starting with 0. For example, to convert the binary value 1010011100 from the table above, first separate the digits as: 1 010 011 100. Then multiply the values as follows:

1. 0x1 + 0x2 + 1x4 = 4
2. 1x1 + 1x2 + 0x4 = 3
3. 0x0 + 1x2 + 0x4 = 2
4. 1x1 + 0x2 + 0x4 = 1

The resulting value is: oct 1234. Octal values may also be displayed with a subscript "8," such as 1234₈. The bottom row of the table above can be written in subscript notation as:

1010011100₂ = 1234₈ = 668₁₀ = 29C₁₆