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.

Step-by-Step Conversion Examples

Setting Linux File Permissions with chmod

The most common real-world use of octal today is Unix/Linux file permissions. The command chmod 755 script.sh sets:

• Owner (7 = 111₂): read (4) + write (2) + execute (1) = rwx
• Group (5 = 101₂): read (4) + execute (1) = r-x
• Others (5 = 101₂): read (4) + execute (1) = r-x

The permission string displays as -rwxr-xr-x in ls -la. Common permission sets:

• 644: Owner read+write, group+others read only — typical for config files
• 755: Owner full, group+others read+execute — typical for directories and executables
• 600: Owner read+write only — typical for SSH private keys
• 400: Owner read only — certificate files and secrets

Binary breakdown of 644: 6 = 110 (rw-), 4 = 100 (r--), 4 = 100 (r--) → displays as rw-r--r--. Understanding the binary mapping makes permission numbers intuitive rather than arbitrary codes to memorize.

Decimal to Octal Conversion: A Worked Example

Convert 365 (decimal) to octal using repeated division by 8:

• 365 ÷ 8 = 45 remainder 5
• 45 ÷ 8 = 5 remainder 5
• 5 ÷ 8 = 0 remainder 5
• Reading remainders bottom-up: 555 in octal

Verification: 5×64 + 5×8 + 5×1 = 320 + 40 + 5 = 365 ✓

The coincidence that 365 = 555₈ makes it a useful mnemonic — 365 days in a common year. Another memorable pair: 255 decimal = 377 octal (the maximum one-byte value), and 256 decimal = 400 octal (the beginning of the next "century").

Binary to Octal: The Three-Bit Grouping Method

Binary converts to octal directly by grouping bits in threes from the right — no multiplication needed. Convert binary 110 101 001 to octal:

• 110 → 6
• 101 → 5
• 001 → 1
• Result: 651 in octal

Verification: 6×64 + 5×8 + 1 = 384 + 40 + 1 = 425 decimal. Binary check: 256+128+32+8+1 = 425 ✓

This grouping method works because 8 = 2³ — each octal digit maps to exactly 3 binary bits. Hexadecimal (base 16 = 2⁴) groups bits in fours, which aligns better with 8-bit bytes (two hex digits per byte). This alignment advantage is why hex replaced octal in modern computing after 8-bit architectures became dominant in the late 1970s.

Octal in Programming Languages

Octal literals appear in several programming languages with different syntax — knowing the convention prevents subtle bugs:

• C/C++/Java: A leading zero means octal. 017 = 15, not 17. Classic source of beginner bugs.
• Python 3: 0o17 = 15 (explicit 0o prefix; Python 2's leading-zero syntax was removed)
• JavaScript: Strict mode prohibits legacy 017; use 0o17 instead
• Go: 0755 in older code; 0o755 preferred since Go 1.13

A real-world pitfall in C: chmod(path, 0644) correctly uses octal 644 (rw-r--r--). But if a developer writes chmod(path, 0844) intending "owner read+execute + group read + others read," they actually pass octal 844 = decimal 548 — which maps to unusual permission bits. Always use the explicit 0o prefix in Python and Go 1.13+, and double-check octal literals in C with a converter when in doubt.

Source: IEEE POSIX.1 standard (file permissions); programming language specifications (C11, Python 3, ECMAScript 2022). Last verified: May 2026.