Octal to Binary Converter

What the octal to binary converter does

This expands an octal number into the binary it stands for. Type the octal in, press the button, and copy out the 0s and 1s.

Most often you do this to see what an octal value really is at the bit level, and the most common reason of all is to read a file permission down to its individual read, write, and execute switches.

How to use it

1. Enter your octal number. Use only the digits 0 to 7, for example 755.
2. Press Convert. The binary version appears in the output box.
3. Click the result to copy it. Tap the output to copy it to your clipboard.

Press Reset to clear both boxes.

Each octal digit is three bits

Because an octal digit only ever runs from 0 to 7, it fits exactly into three bits. So this conversion is digit by digit: take each octal digit on its own, write its three-bit pattern, and join all the pieces in order. One octal digit in, three bits out, with no arithmetic across the whole number.

A worked example with real numbers

Take 755. Handle each digit separately.

• 7 is 111 in three bits.
• 5 is 101 in three bits.
• 5 is 101 in three bits.

Join them in order: 111101101. So 755 in octal is 111101101 in binary. Each digit unfolded into its own three bits, nothing more.

The eight patterns

There are only eight three-bit patterns to know, one for each octal digit, and they are quick to memorize.

Each octal digit always becomes a full three bits, leading zeros included, so 2 is 010 rather than just 10. Keeping all three is what keeps the groups aligned when you join them.

Reading a permission down to its switches

This is the everyday use. A permission like 755 hides three switches per group, and expanding it shows them plainly. The bits are 111 101 101, and each three-bit group maps to read, write, execute: 111 is read, write, and execute, while 101 is read, execute, and no write. So 755 spells out as rwx for the owner and r-x for both group and others. The expansion turns a three-digit number into the exact list of who can do what.

Questions people ask

How do I convert octal to binary by hand?

Take each octal digit on its own, write its three-bit pattern, and join the patterns in order. There is no arithmetic across the whole number.

Do I keep the leading zeros in each group?

Yes, within each digit. Every octal digit becomes a full three bits, so 2 is 010 and 1 is 001. Keeping all three keeps the groups aligned.

Why does each octal digit give three bits?

Because an octal digit ranges over 0 to 7, and three bits cover exactly that range, so one digit fits neatly into three bits.

What does 755 look like in bits?

111101101, which groups as 111 101 101. Read as permissions, that is rwx for the owner and r-x for group and others.

References

1. Weisstein, Eric W. "Binary." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Binary.html
2. IEEE and The Open Group. chmod, change the file modes. The Open Group Base Specifications (POSIX.1-2017). https://pubs.opengroup.org/onlinepubs/9699919799/utilities/chmod.html