Binary to Octal Converter

How to Convert Binary to Octal

Converting binary to octal 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. Starting from the right, split the binary number into groups of 3 digits. Pad the leftmost group with leading zeros if it is short.
2. Write the place values 4, 2, 1 underneath each group.
3. In every group, add the place values wherever the bit is 1.
4. Convert each group total into a single octal digit.
5. Write the octal digits in the same left to right order as the groups.

Worked example: 111101101

Result: (111101101)² = (755)⁸

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.

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.

Binary to Octal Conversion Examples

Binary to Octal 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.