The Octal Number System: What is Base 8 and When is it Used?

What is Octal?

Octal is a base-8 number system that uses digits 0 through 7. Unlike decimal (base 10) or binary (base 2), octal groups binary digits into sets of three, which made it a natural shorthand for older computing systems.

Why Was Octal Used in Computing?

Before hexadecimal became the standard, octal was widely used in early computing — particularly with 6-bit, 12-bit, and 36-bit architectures (which divided evenly into groups of 3 bits). Some early programming languages and Unix/Linux systems still use octal today for file permissions.

Unix File Permissions in Octal

If you've ever used chmod 755 or chmod 644 on a Linux system, you've used octal. Each digit represents three bits for owner, group, and others:

• 7 = 111 in binary = read + write + execute
• 6 = 110 in binary = read + write
• 5 = 101 in binary = read + execute
• 4 = 100 in binary = read only
• 0 = 000 in binary = no permissions

Octal to Decimal Conversion

Example: 57 in octal

• 5 × 8^1 = 40
• 7 × 8^0 = 7
• Total: 40 + 7 = 47 in decimal

Binary to Octal Shortcut

Group binary digits into sets of 3 from the right, then convert each group to a single octal digit.

• Binary: 101 111 → Octal: 5 7 → Octal 57

Convert between octal, decimal, binary and hex instantly with our number system converter.