How do you convert octal to binary?

Each octal digit (0–7) maps to exactly three binary digits. For example, octal 7 = binary 111, octal 5 = binary 101. Replace every octal digit with its 3-bit group, then concatenate all groups and remove any leading zeros.

What octal digits are valid?

Valid octal digits are 0 through 7. The digits 8 and 9 do not exist in octal. This tool highlights any invalid characters in your input.

Why does each octal digit become 3 binary bits?

Because 2³ = 8, so three binary bits can represent exactly the same range (0–7) as one octal digit. This 1-to-3 correspondence makes octal a compact shorthand for binary.

What is the binary equivalent of octal 755?

7 = 111, 5 = 101, 5 = 101, so octal 755 = binary 111101101. In Unix permissions this means rwxr-xr-x.

Can I convert negative octal numbers?

Enter the numeric magnitude without a minus sign. Negative number representation depends on the context (sign-magnitude, two's complement, etc.) and is beyond the scope of a simple base conversion.

Octal to Binary Converter

Name: Octal to Binary Converter
Availability: InStock
Author: Nham Vu

Convert any octal (base-8) number to its binary (base-2) equivalent instantly, with a digit-by-digit breakdown.

Octal Input

Octal number (digits 0–7)

Quick examples

Binary Result

Enter an octal number on the left to see the binary output.

Batch Converter

One octal number per line. Results appear on the right.

Octal values

Binary results

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Summary

Convert any octal (base-8) number to its binary (base-2) equivalent instantly, with a digit-by-digit breakdown.

How it works

Enter one or more octal digits (0–7) in the input field.
Each octal digit is independently mapped to its 3-bit binary equivalent.
The binary groups are concatenated and leading zeros are stripped from the result.
The decimal equivalent is shown alongside for cross-reference.
Use the batch mode to convert a list of octal numbers at once.

Use cases

Convert Unix file permission octals (e.g. 755) to binary for analysis.
Verify octal-to-binary mapping exercises in computer science courses.
Debug embedded systems that store values in octal registers.
Convert octal color codes or memory addresses to binary.
Study number base conversion for programming interviews.
Quickly verify hand-calculated octal-to-binary conversions.

Frequently Asked Questions

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Last updated: 2026-05-29 · Reviewed by Nham Vu