Octal to Binary Converter

How to Convert Octal to Binary?

To convert octal to binary, replace each octal digit with its 3-bit binary equivalent (000 to 111) and concatenate the groups. Remove any leading zeros if necessary. For example: 753₈ → 7=111, 5=101, 3=011 → 111101011₂.

What is Octal?

Definition

Octal (base-8) is a positional numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.

Common Uses

• Early computer systems and minicomputers
• Unix and Linux file permission notation
• Compact representation of binary values
• Digital electronics and microcontroller documentation

Relationship to Binary

Each octal digit corresponds exactly to a group of three binary digits. This enables a straightforward conversion between octal and binary by mapping each digit individually.

What is Binary?

Definition

Binary (base-2) is a numeral system that uses only two digits: 0 and 1. It is the fundamental language of computers and digital electronics.

Common Uses

• Computer data storage and processing
• Digital electronics and circuits
• Network communication protocols
• Machine code and assembly language
• Boolean logic and decision-making
• Error detection and correction codes

Structure

Each binary digit (bit) represents a power of 2. From right to left: 2⁰, 2¹, 2², 2³, etc. For example, 1010₂ = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10₁₀.

Octal to Binary Conversion Table

This table shows common octal to binary conversions for quick reference.