Binary to Octal Conversion

Use this converter to easily convert binary numbers into octal values and vice versa.

How to Use This Converter

• Enter a binary number (base-2) to see its octal equivalent
• Or input an octal number (base-8) to convert it to binary

This converter supports both directions: binary to octal and octal to binary.

Understanding the Conversion

Binary is base-2 and uses only 0s and 1s, while octal is base-8 and uses digits from 0 to 7. Each group of 3 binary digits corresponds to 1 octal digit. This makes binary-to-octal conversion quick and efficient without needing to go through decimal first.

Binary to Octal Grouping

To convert binary to octal:

1. Start from the right and split the binary number into groups of 3 bits
2. Add leading zeros to the leftmost group if needed to make a complete group of 3
3. Convert each group to its octal value

Example grouping:

Binary:     101110011 (9 bits)
Grouped:    000 101 110 011
Octal:      0    5   6   3 → 0563

Example

Convert the binary number 100111 to octal:

1. Group into 3s: 100 111
2. Convert each: 4 7

Result: 1001112 = 478

Additional example conversions:

Why Use Octal?

Before hexadecimal became the standard, octal was widely used in early computing systems, especially with systems based on 12-bit, 24-bit, or 36-bit architectures.

Octal offers a more human-readable format than binary while maintaining a straightforward mapping—each octal digit represents exactly 3 bits.

Octal is still used today in areas like:

• File permissions in Unix/Linux systems (e.g., chmod 755)
• Embedded systems and microcontrollers
• Instruction sets and legacy computing systems