base8

Base8, commonly known as octal, is a numeral system that uses eight digits: 0 through 7. In base-8, each digit represents a power of eight, so a number is expressed as a sum of digits times powers of eight. For example, the octal number 127 represents 1×8^2 + 2×8^1 + 7×8^0 = 64 + 16 + 7 = 87 in decimal.

Historically, octal arose in early computing because binary data could be grouped into sets of three bits; eight combinations align with a single octal digit. This made octal convenient for representing binary values. It was widely used on some minicomputers and early Unix systems. Unix file permissions are commonly shown in octal (e.g., 755).

A practical note: many programming languages indicate octal literals with a leading zero (in C) or a 0o/0O prefix (in Python). Each octal digit corresponds to exactly three binary digits, so conversion between binary and octal is straightforward.

Today hexadecimal (base-16) and binary are more common in general-purpose computing, but octal remains in use for specific legacy systems and as a human-friendly way to view certain bit fields, especially in permissions and file modes in Unix-like systems.

See also binary, base-2, base-16, and the octal numeral system.