Convert Octal to Decimal

Octal (base 8) uses digits 0 through 7. While less common than hex in modern computing, octal remains important for Unix/Linux file permissions and appears in some legacy systems and programming contexts.

Step-by-step example — converting 7524 (octal) to decimal:

1. Write each digit with its position: 7(3) 5(2) 2(1) 4(0)
2. Multiply by powers of 8: 7×8³ + 5×8² + 2×8¹ + 4×8⁰
3. Calculate: 7×512 + 5×64 + 2×8 + 4×1
4. Sum: 3584 + 320 + 16 + 4 = 3924

So 7524₈ = 3924₁₀.

Octal in Unix file permissions:

The most common place you will encounter octal today is in Unix/Linux file permissions. The command chmod 755 file uses octal notation:

• 7 = 111₂ — owner: read + write + execute
• 5 = 101₂ — group: read + execute
• 5 = 101₂ — others: read + execute

Each octal digit maps to exactly 3 binary bits, which perfectly represents the three permission bits (rwx) for each user class.

Octal in programming languages:

• In C and C++, octal literals start with a leading zero: 0755
• In Python 3, octal uses the 0o prefix: 0o755
• In JavaScript, strict mode requires 0o755
• The C library function printf uses %o to format numbers in octal

Historical context:

Octal was more popular in early computing when machines used word sizes that were multiples of 3 bits (like the PDP-8 with 12-bit words). Each octal digit represented 3 bits cleanly. As 8-bit bytes and 16/32/64-bit words became standard, hex (4 bits per digit) largely replaced octal for general use. However, octal persists in file permissions and some telecommunications protocols.