Octal Number System & Conversion Guide

What is Octal?

Octal is base 8, using digits 0 through 7 only. Each position is a power of 8. Historically popular in computing when systems used 12-bit, 24-bit, or 36-bit word sizes divisible by three, octal provided compact notation with three binary bits per octal digit.

Octal to Decimal

Multiply each digit by 8 raised to its position (rightmost = 0).

Example: 377₈ = 3×64 + 7×8 + 7×1 = 192 + 56 + 7 = 255 decimal.

Decimal to Octal

Repeatedly divide by 8; read remainders bottom-to-top.

Example: 255 → 255÷8=31 R7 → 31÷8=3 R7 → 3÷8=0 R3 → 377 octal.

Octal ↔ Binary

Each octal digit = exactly three binary bits.

377 octal → 011 111 111 binary → 11111111 (drop leading 0) = 255.

Octal	Binary
0	000
7	111

Unix File Permissions (chmod)

chmod 755 file sets permissions: owner 7 (rwx), group 5 (r-x), others 5 (r-x). Each digit is octal: 7=111 (read+write+execute), 5=101 (read+execute).

Tools

Convert all bases with the Number System Converter. See also the Number System Guide.

Common Mistakes

• Using digits 8 or 9 in octal (invalid)
• Grouping binary in fours instead of threes for octal conversion
• Confusing octal 10 (eight decimal) with decimal 10

Frequently Asked Questions

Is octal still used today?

Yes — primarily Unix/Linux permissions, some legacy documentation, and educational curricula.

How is octal different from hex?

Octal groups 3 bits per digit; hex groups 4. Hex is more common in modern programming.

What is octal 10 in decimal?

10₈ = 1×8 + 0 = 8 decimal.

Can I convert octal to hex directly?

Convert octal → binary (3 bits per digit) → group binary in fours → hex. Or use our converter.

What octal value represents read-only for owner?

4 octal = 100 binary = read only (r—).