Octal to Binary Converter

What is Octal to Binary Conversion?

Octal to binary conversion turns a base-8 number (digits 0-7) into its base-2 equivalent. Because 8 is exactly 2³, each octal digit maps to precisely 3 binary bits — there is no need to convert through decimal.

For example, octal 52 converts digit by digit: 5 → 101, 2 → 010, giving 101010. For the reverse operation, see the Binary to Octal Converter. Want to learn how to convert octal to binary manually? Read the full step-by-step guide.

Why Each Octal Digit Is 3 Binary Bits

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

Octal digit to binary reference

Worked example: 52₈

5 → 101
2 → 010

Combine: 101 010
52₈ = 101010₂

When digits are combined, any leading zeros in the first group can be dropped from the final result — for example, octal 12 converts to 001 010, which is 1010 once the leading zeros are removed.

Octal to Binary Conversion Table

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

Octal in Unix/Linux File Permissions

The most common practical use of octal is Unix/Linux file permissions (chmod). Each of the three octal digits covers owner, group, and others, and each digit's bits map to read (4), write (2), and execute (1):

Where Octal to Binary Conversion Is Used

• Unix/Linux system administration: reading chmod permission values as their underlying read/write/execute bits.
• Legacy systems and documentation: some older systems and file formats express values in octal, which still needs converting to binary for bit-level analysis.
• Low-level programming and debugging: inspecting register values or debug output expressed in octal to see which individual bits are set.
• Computer science education: octal-to-binary conversion is a clear, direct way to demonstrate how positional number systems relate to each other.

Related Converters

Frequently Asked Questions