Octal to Binary Converter

Convert octal numbers to binary code. This tool expands each octal digit into its 3-bit binary form. Useful for interpreting octal-based systems like Unix file permissions.

Octal Input

Binary Output

Octal to Binary Reference Table

Octal

Binary

Octal

Binary

000

100

001

101

010

110

011

111

How Octal to Binary Conversion Works

Each octal digit (0-7) maps directly to a 3-bit binary number. Simply replace each octal digit with its 3-bit binary equivalent. For example: 755 = 7(111) 5(101) 5(101) = 111101101 in binary.

Octal is commonly used for Unix file permissions where each digit represents read (4), write (2), and execute (1) permissions.

How It Works

This octal to binary converter transforms octal numbers (base-8) into binary code (base-2). Each octal digit (0-7) maps directly to exactly 3 binary bits, making conversion straightforward and efficient.

The conversion process:

Validate input: Ensure input contains only valid octal digits (0-7).
Map each digit: Convert each octal digit to its 3-bit binary equivalent (0=000, 7=111).
Concatenate bits: Join all 3-bit groups to form the complete binary string.
Optional padding: Add leading zeros to maintain bit alignment if needed.

For example: 755 (octal) becomes 111 101 101 in binary. This direct mapping made octal popular for representing binary data, especially in Unix file permissions.

When You'd Actually Use This

Unix File Permissions

Convert octal permission codes (755, 644) to binary to understand read/write/execute bits.

Legacy System Analysis

Work with older systems that used octal notation for binary data representation.

Digital Electronics

Convert octal values from datasheets or documentation to binary for circuit design.

Learning Number Systems

Understand the relationship between octal and binary for computer science education.

Aviation Transponder Codes

Convert aircraft transponder codes (squawk codes) from octal to binary for analysis.

Programming Debugging

Interpret octal literals in code (0755 in C/Python) and understand their binary values.

What to Know Before Using

Each octal digit = 3 binary bits

This is the key relationship. Octal is a compact representation of binary, with 3 bits per digit.

Only digits 0-7 are valid

Octal is base-8, so digits 8 and 9 are invalid. If you see them, it's not octal.

Leading zeros may be significant

In programming, leading 0 often indicates octal (0755 = octal 755). In pure math, leading zeros don't change value.

Output length is predictable

N octal digits always produce 3×N binary bits. 4 octal digits = 12 binary bits.

Unix permissions use special meaning

Each 3-bit group represents read(4), write(2), execute(1) for user/group/others.

Common Questions

What's the binary for octal 7?

7 (octal) = 111 (binary). It's the maximum 3-bit value. Octal digits 0-7 map to binary 000-111.

How do I convert binary back to octal?

Group binary into 3-bit nibbles from right, then convert each to octal. 111101101 becomes 755.

Why was octal popular in computing?

Early computers used 12, 24, or 36-bit words - divisible by 3. Octal was more compact than binary. Hex later replaced it for 8-bit systems.

What's the octal to binary table?

0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. Memorize these 8 conversions.

What does chmod 755 mean in binary?

7=111 (rwx), 5=101 (r-x), 5=101 (r-x). Owner: read+write+execute. Group/Others: read+execute.

Is octal still used today?

Less than hex, but still in Unix file permissions, some legacy systems, and aviation. Hex is more common for modern computing.

Can octal represent negative numbers?

Yes, using the same methods as binary (sign bit or 2's complement). The representation is just a different notation.

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