Octal to Decimal Converter

About the Octal to Decimal Converter

The Octal to Decimal Converter translates octal (base-8) numbers into decimal (base-10), hexadecimal (base-16), and binary (base-2). Enter a number using digits 0–7 and review the converted values with a step-by-step expansion.

Octal was historically important in computing because early systems used 12-bit, 24-bit, or 36-bit words that divided evenly into 3-bit groups. Today, octal is most commonly encountered in Unix/Linux file permissions (chmod values like 755 or 644) and some programming languages.

Each octal digit represents exactly 3 binary bits, making octal-to-binary conversion particularly straightforward. This converter also shows the hex and binary equivalents and provides the mathematical expansion for educational use.

When This Page Helps

Unix permissions, older computing systems, and number theory all use octal. It shows cross-base conversion with a step-by-step explanation for learning.

How to Use the Inputs

1. Enter an octal number (digits 0–7 only).
2. View the decimal equivalent in the result panel.
3. Check the hexadecimal and binary representations.
4. Review the positional expansion for learning.
5. Use for chmod permission calculations (e.g., 755 = rwxr-xr-x).

Example Calculation

Tips & Best Practices

• Each octal digit converts to exactly 3 binary bits — no calculation needed.
• Unix chmod 755 means owner=rwx(7), group=r-x(5), others=r-x(5).
• chmod 644 means owner=rw-(6), group=r--(4), others=r--(4).
• Octal is less common today but still appears in Unix, C/C++ literals (prefix 0), and some legacy systems.
• In C, a leading zero like 0777 denotes an octal literal — a common source of bugs.

Octal in Computing History

Octal was dominant in early computing when many machines used 12, 24, or 36-bit word sizes. The PDP-8, one of the most successful minicomputers, used 12-bit words displayed in octal. The shift to 8-bit bytes and 32/64-bit words made hexadecimal (4 bits per digit) more natural than octal (3 bits per digit).

Unix File Permissions

The most visible modern use of octal is Unix file permissions. Three permission bits (read=4, write=2, execute=1) form a 3-bit number for each of owner, group, and others. chmod 644, chmod 755, and chmod 777 are everyday commands for system administrators.

Octal Literals in Code

In C/C++, a leading zero indicates an octal literal: 010 = 8 in decimal, not 10. Python 3 uses the 0o prefix: 0o10 = 8. JavaScript's strict mode disallows legacy octal literals to prevent confusion.

Frequently Asked Questions

• What is the octal number system?

  Octal is a base-8 number system using digits 0–7. Each digit represents three binary bits. It was widely used in early computing when word sizes were multiples of 3 bits. Today it's primarily used for Unix file permissions.

• How do I convert octal to decimal?

  Multiply each octal digit by 8 raised to its position (starting from 0 on the right) and sum the results. For 752: 2×1 + 5×8 + 7×64 = 2 + 40 + 448 = 490.

• What does chmod 755 mean?

  In Unix, 755 is an octal representation of file permissions. 7 (111 binary = rwx) for owner, 5 (101 binary = r-x) for group, and 5 for others. This means the owner can read, write, and execute; group and others can read and execute.

• How do I convert octal to binary?

  Replace each octal digit with its 3-bit binary equivalent: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. So 755 = 111 101 101.

• Why do some programming languages use octal?

  C, C++, Java, and Python support octal literals (usually with a 0 or 0o prefix). This is mainly for backward compatibility and for Unix permission values. A common bug is accidentally writing 0100 (octal 64) when you meant decimal 100.

• Is octal still relevant today?

  Octal is less common but still relevant for Unix/Linux file permissions (chmod), some legacy systems, and as an intermediate step in binary-to-decimal conversion. Most modern systems prefer hexadecimal for compact binary representation.