Binary to Octal Converter

What the binary to octal converter does

This turns a binary number into octal, the base-8 system. Type the 0s and 1s in, press the button, and copy out the octal.

Like hex, octal lines up cleanly with binary, so the conversion is a matter of grouping rather than arithmetic. The difference is the group size, and where you tend to use the result.

How to use it

1. Enter your binary number. Type the 0s and 1s, for example 11111111.
2. Press Convert. The octal 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.

The three-bit trick

Where hex pairs with four bits, octal pairs with three. Eight is two to the third power, so a group of three bits counts from 0 to 7, which is exactly the range of a single octal digit. So you split the binary into groups of three bits, starting from the right, and turn each group into one octal digit. Three bits in, one octal digit out.

A worked example with real numbers

Take 11111111, a full byte of 1s. Split it into threes from the right. Eight bits do not divide evenly into three, so the leftmost group is short and gets padded: 011, 111, 111.

• 011 is 3.
• 111 is 7.
• 111 is 7.

So 11111111 in binary is 377 in octal. As a check, both come to 255 in decimal, which is the most a single byte can hold.

When the bits do not divide by three

As in the example above, the bit count is often not a clean multiple of three. You handle it the same way every time: pad the leftmost group with 0s on the left until it has three bits. Since leading zeros never change a value, the answer stays exact. For instance, the seven-bit 1101101 pads to 001, 101, 101, which reads as 155 in octal.

The permissions connection

This three-bit grouping is exactly why Unix file permissions are written in octal. A permission group is three switches, read, write, and execute, which is three bits, which is one octal digit. So a nine-bit permission pattern falls naturally into three octal digits. The bits 111101101 group into 111, 101, 101, which is 755, the familiar setting where the owner can read, write, and execute, and everyone else can read and execute. The grouping you just did by hand is the same one happening behind a chmod command.

Questions people ask

How do I convert binary to octal by hand?

Split the binary into groups of three bits starting from the right, pad the leftmost group with leading zeros if needed, then turn each three-bit group into its single octal digit.

What if the bits do not group evenly into threes?

Pad the leftmost group with 0s on the left until it is three bits. Leading zeros do not change the value, so the result stays correct.

Why three bits per octal digit?

Because eight is two cubed, so three bits cover exactly the values 0 to 7, which is the full range of one octal digit.

Why does this matter for file permissions?

Because each permission group, read, write, and execute, is three bits, and three bits is one octal digit. That is why permission settings like 755 are written in octal.

References

1. Weisstein, Eric W. "Octal." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/Octal.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