Binary to Octal Converter

What Is Binary to Octal Conversion?

Binary to octal conversion turns a base-2 number (digits 0 and 1) into its base-8 equivalent (digits 0-7). Because 8 is exactly 2³, every group of 3 binary bits maps to exactly one octal digit — there is no need to convert through decimal.

For example, binary 101010 groups as 101 010, which converts digit by digit to 5 2, giving octal 52. For the reverse operation, see the Octal to Binary Converter.

Why Each Octal Digit Is 3 Binary Bits

Three binary bits represent exactly 8 possible values (000 through 111), and one octal digit also represents exactly 8 possible values (0 through 7). Since the ranges match, converting binary to octal is grouping and direct substitution — no arithmetic across digits is required.

Binary to octal digit reference

Worked example: 101010₂

Group from the right into 3-bit chunks:
101 010

Convert each group:
101 → 5
010 → 2

Combine: 5 2
101010₂ = 52₈

When the leftmost group has fewer than 3 bits, pad it with leading zeros before converting — for example, binary 1010 is grouped as 001 010, giving octal 12. The leading zeros only affect grouping and don't change the value.

Binary to Octal Conversion Table

A quick reference for common binary numbers and their octal, decimal, and hexadecimal equivalents:

Where Binary to Octal Conversion Is Used

• Computing education: binary-to-octal conversion is a direct way to demonstrate how positional number systems relate to each other, without the extra step of converting through decimal.
• Low-level systems and debugging: some debuggers, memory dumps, and register displays use octal grouping to make long binary values easier to read.
• Legacy notation: older systems built around 12-bit, 24-bit, or 36-bit words used octal because those word sizes divide evenly by 3; some of that documentation and tooling still uses it today.
• Bit grouping for Unix permissions: Unix/Linux file permissions (chmod) are written in octal, with each digit representing 3 permission bits (read, write, execute) for owner, group, and others — for example, 111 101 101 is 755.

Related Converters

Frequently Asked Questions