Octal

Octal is a base-8 numeral system that uses eight symbols: 0 through 7. Like other positional numeral systems, the value of a digit is its face value multiplied by eight raised to the power of its position. In octal, each digit represents three binary digits, since 2^3 equals 8, which makes octal convenient for representing binary data. Converting between octal and binary is straightforward by grouping bits in sets of three.

Historically, octal was widely used in early computing and computer engineering, particularly where binary data could be conveniently displayed or stored in groups of three bits. In modern computing, hexadecimal has largely supplanted octal for low-level representations, but octal remains in use in specific contexts, notably in Unix-like systems for file and directory permissions. In the permission model, the three-bit sets for user, group, and others are encoded as three octal digits, for example 755, where each digit represents read, write, and execute permissions.

Notation varies by language: many languages denote octal literals with a leading zero (for example 0755 in C); Python 3 uses a 0o or 0O prefix (e.g., 0o755). Decimal values can be converted to octal by repeated division by eight, or by combining octal digits to represent groups of binary bits.

See also: base-8 numeral system; Unix file permissions; binary and hexadecimal representations.