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Octal refers to the base-8 numbering system. It comes from the Latin word for eight. The octal numbering system uses the numerals 0-1-2-3-4-5-6-7. In computing environments, it is commonly used as a shorter representation of binary numbers by grouping binary digits into threes. The chmod command in Linux or UNIX uses octal to assign file permissions.
Octal is another way to count numbers. While humans normally count in tens, and machines count in twos, it is possible to use any number as the basis for counting and calculation. Some Native American tribes have used octal by counting the spaces between fingers. Characters in the 2009 film “Avatar” used octal because they had four fingers on each hand. Some mathematicians have proposed the wider adoption of octal.
Using octal is a convenient way to abbreviate binary numbers. Starting from the right, group all binary digits into sets of three. If the last group on the left does not have three digits, then add a zero. Each three-digit binary group translates into a one-digit octal number.
Start with a binary number:
Group the binary number into threes. Add a zero to the left if necessary:
Convert each three-digit group into an octal number:
Combine the numerals to form the octal number:
Using an octal number instead of a binary number saves digits. In the early days of computing, octal was often used to shorten 12-bit, 24-bit or 36-bit words. Hexadecimal is now more commonly used in programming, making number representations even shorter than octal.
Various symbols have been used in programming languages to designate octal, including the digit 0, the letters o or q, the digit–letter combination 0o, or the symbol & or $. Base-8 can also be shown by using the number 8 as a subscript (for example, 1358).
Perhaps the most prominent use of octal in today’s computing environment is in Linux or UNIX file and directory permissions. Using the chmod command, administrators can assign read, write and execute privileges to users, groups and others.