Binary to Octal Converter

How to Convert Binary to Octal?

To convert binary to octal, group the binary digits into sets of three (from right to left), padding with zeros on the left if needed. Then convert each group to its octal equivalent (0-7). For example: 1101011₂ → (001)(101)(011) → 1 5 3 → 153₈.

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.

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 3-bit grouping makes octal a convenient shorthand for representing long binary sequences.

Binary to Octal Conversion Table

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