Octal to Decimal Converter

How to Convert Octal to Decimal?

To convert octal to decimal, multiply each octal digit by 8 raised to the power of its position (counting from right to left, starting at 0) and sum the results. For example: 377₈ = (3 × 8²) + (7 × 8¹) + (7 × 8⁰) = 3×64 + 7×8 + 7 = 255₁₀.

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 represents exactly three binary digits (bits), allowing for straightforward conversions between the two systems.

What is Decimal?

Definition

Decimal (base-10) is the standard numeral system used in everyday life. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Common Uses

• Everyday counting and arithmetic
• Financial calculations and currency
• Measuring quantities and dimensions
• Scientific calculations
• Data representation in most applications

History

The decimal system is believed to have originated from counting on fingers (humans typically have 10 fingers), making it the most intuitive and widely adopted numeral system.

Octal to Decimal Conversion Table

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