Octal to Binary Converter Online

How to Convert Octal to Binary

Converting octal to binary by hand is straightforward once you know the routine. The converter above does it instantly, but working through the steps yourself is the fastest way to understand what is actually happening to the digits.

1. Take each octal digit on its own.
2. Replace every digit with its 3 digit binary equivalent, keeping leading zeros.
3. Join the groups together in the same order.
4. Drop any leading zeros if you want the shortest form.

Worked example: 755

Result: (755)⁸ = (111101101)²

The Octal System

Octal is the base 8 numeral system and uses the digits 0 through 7. Its usefulness comes from the fact that one octal digit maps exactly onto three binary digits, so it is a compact way to write binary without doing real arithmetic. Octal was common on early minicomputers with 12, 24, and 36 bit words. Today the place most developers still meet it is Unix file permissions, where a command such as chmod 755 sets read, write, and execute bits three at a time.

Octal uses the digits 0 through 7.

The Binary System

Binary is the base 2 numeral system. It uses only two symbols, 0 and 1, and each digit is called a bit. Every digital circuit ever built relies on it, because a transistor has two reliable states, on and off, which map directly onto 1 and 0. Place values double as you move left: 1, 2, 4, 8, 16, 32 and so on. Eight bits make one byte, which can hold 256 distinct values, enough for every character in the original ASCII set.

Binary uses the digits 0 and 1.

Octal to Binary Conversion Examples

Octal to Binary Conversion Chart

A full reference table for the values 1 to 256. Use it to check a conversion quickly or to look up a common value without typing anything.

Need a different pair of bases? Browse every number converter tool including binary, octal, decimal, and hexadecimal in both directions.