Binary to Octal Converter

How Binary to Octal Conversion Works

The binary to octal conversion follows the same grouping principle as hex, but with groups of 3 bits instead of 4. Since 2^3 = 8, each group of three binary digits maps directly to one octal digit (0-7). This makes the conversion mechanical and easy to do by hand once you know the 3-bit patterns.

For example, take 110101. Group by threes from the right: 110 101. 110 in binary is 6 in decimal = octal digit 6. 101 in binary is 5 in decimal = octal digit 5. So 110101 in binary equals 65 in octal. I don't use octal as much as hex in my daily work, but it still shows up in important places. Unix file permissions (chmod 755, 644), for instance, are octal numbers. When you run stat -c "%a %n" on a Linux system and see 644, that's an octal representation of the permission bits — rw-r--r-- in human terms.

Step-by-Step Binary to Octal Conversion

1. Group into 3s — Starting from the rightmost bit, group binary digits into sets of three. Add leading zeros to the leftmost group if needed.
2. Convert each group — Each 3-bit group maps to a single octal digit (0-7).
3. Concatenate — Combine the octal digits in order.

Example: 1011010 → Pad to 001 011 010 → 1 + 3 + 2 → 132 in octal.

3-Bit Group Reference

• 000 = 0, 001 = 1, 010 = 2, 011 = 3
• 100 = 4, 101 = 5, 110 = 6, 111 = 7

Where Octal is Still Used Today

While hex is more common in modern computing, octal still has its place. Beyond Unix file permissions — which is probably the most common real-world octal use case — you'll find octal in some legacy file formats, certain network protocols, and specific embedded systems. Some older programming textbooks use octal for teaching binary concepts because the 3-bit grouping is slightly simpler for beginners than the 4-bit hex grouping.

One thing I found interesting early in my career was that some character encoding schemes from the 60s and 70s used octal notation in their documentation. The ASCII table, for example, shows some characters in octal in older references. A is 101 in octal — which is 1000001 in binary. Having a solid binary to octal converter handy makes these historical references a lot easier to work with. And if you're ever doing forensics work on old Unix systems or PDP-11 era computers — and yes, people still maintain those — octal is the native language.