Binary to Octal Converter

2

Conversion Result

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3-Bit Grouping

Convert binary numbers to octal by grouping bits into 3-bit sets. See step-by-step how each group maps to an octal digit — commonly used in Unix file permissions and legacy systems.

5Number Systems
∞Precision
0msLatency

What is Binary to Octal Converter?

The Binary to Octal Converter is a tool that transforms binary numbers (base 2) into octal (base 8) representation. Since 8 is a power of 2 (2³), every 3 binary digits map directly to one octal digit, making the conversion a straightforward grouping process without complex arithmetic.

This tool exists because the octal number system remains important in several areas of computing and engineering. It is most notably used in Unix/Linux file permissions (e.g., chmod 755), aviation transponder codes, and legacy computing systems. Understanding binary-to-octal conversion helps system administrators, developers, and students work more efficiently with these systems.

Our converter instantly groups your binary input into 3-bit sets, maps each group to its octal digit, and provides a clear visual breakdown — turning what could be a tedious manual process into an instant, educational experience.

Interactive Demo

Binary to Octal Converter Formula

Type a binary number below. The engine groups it into 3-bit sets from the right and maps each group to an octal digit (0–7).

3-Bit Grouper
Practical Application

Unix File Permissions Decoder

Unix file permissions use octal notation — each digit encodes 3 permission bits: r (read = 4), w (write = 2), x (execute = 1).

The command chmod 755 sets: Owner = 7 (rwx), Group = 5 (r-x), Others = 5 (r-x). Each octal digit maps directly to a 3-bit binary value.

Common Permissions 777 = full access | 644 = read-only files | 755 = executable scripts
chmod Decoder
Owner
r w x
111
Group
r - x
101
Others
r - x
101
Quick Reference

Complete 3-Bit-to-Octal Mapping

All 8 possible 3-bit combinations and their octal digit equivalents.

000
0
(0₈)
001
1
(1₈)
010
2
(2₈)
011
3
(3₈)
100
4
(4₈)
101
5
(5₈)
110
6
(6₈)
111
7
(7₈)
More

Other Number System Conversions

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FAQ

Frequently Asked Questions

How do you convert binary to octal?
Group the binary digits into sets of 3 starting from the right (pad with leading zeros if needed). Then convert each 3-bit group to its octal equivalent: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. Example: 110101₂ → 110 101 → 65₈.
Why does binary to octal use 3-bit groups?
Octal is base 8, and 8 = 2³. This means exactly 3 binary digits map to 1 octal digit. This direct power-of-2 relationship makes conversion a simple grouping-and-replacement process without any arithmetic.
What is the octal number system?
The octal number system is a base-8 numeral system using digits 0 through 7. Each position represents a power of 8. It was historically popular in computing because early computers used 12-bit, 24-bit, or 36-bit words that divide evenly into 3-bit (octal) groups.
Where is octal used today?
Octal is primarily used in Unix/Linux file permissions (e.g., chmod 755), some programming languages (C/C++ octal literals like 0755), and in aviation transponder codes (squawk codes). It was historically important in early computing but has largely been replaced by hexadecimal.
What is the octal equivalent of binary 111111?
Binary 111111₂ = octal 77₈. Grouping into 3-bit sets: 111 111 → 7 7. This is equivalent to decimal 63. In Unix permissions, 77₈ would represent read, write, and execute permissions.
How is octal different from hexadecimal?
Octal is base 8 (digits 0-7, groups of 3 bits), while hexadecimal is base 16 (digits 0-F, groups of 4 bits). Hexadecimal is more common in modern computing because it maps cleanly to bytes (2 hex digits = 1 byte). Octal was more popular with older computer architectures.
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