Free Binary to Octal Converter

Binary to Octal Converter

Free & Instant - Convert binary numbers (base 2) to octal numbers (base 8) for Unix systems, file permissions, and legacy computing

Binary to Octal Converter

Only 0s and 1s allowed

Binary (Base 2)
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Binary Number System

Binary uses only digits 0 and 1, representing the fundamental language of computers and digital electronics. Each position represents a power of 2.

Octal (Base 8)
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Octal Number System

Octal uses digits 0-7, providing a compact representation of binary data. Commonly used in Unix file permissions and legacy computer systems.

Why Convert Binary to Octal?

Unix File Permissions

Essential for understanding and setting file permissions in Unix/Linux systems, where rwx permissions are represented in octal format.

Legacy System Support

Important for maintaining and working with older computer systems and assembly languages that use octal notation.

Data Compression

Useful for representing binary data in a more compact form than pure binary while maintaining readability.

Educational Purpose

Helps students understand different number systems and their relationships in computer science and mathematics education.

How It Works

1. Enter Binary

Input your binary number using only 0s and 1s in the converter field.

2. Group & Convert

System groups binary digits into sets of 3 and converts each to octal digits.

3. Get Octal Result

Copy your octal result for use in Unix systems or legacy applications.

Frequently Asked Questions

How do I convert binary to octal manually?

Group binary digits into sets of 3 (from right to left), then convert each group to its octal equivalent. For example, binary 101110 becomes 101|110, which converts to 56 in octal.

Why is octal base-8 useful in computing?

Octal provides a more compact representation than binary while maintaining a clean relationship (1 octal digit = 3 binary digits). It's historically used in Unix file permissions and some assembly languages.

What's the relationship between binary and octal?

Each octal digit represents exactly 3 binary digits. This makes conversion straightforward: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7.

How do I handle binary numbers not divisible by 3?

When binary length isn't divisible by 3, add leading zeros to complete the leftmost group. For example, 10111 becomes 010|111, converting to 27 in octal.

Is binary to octal conversion exact?

Yes, binary to octal conversion is completely exact with no precision loss. Both number systems represent the same values, just in different bases (2 vs 8).