Decimal to Octal Converter

How to Convert Decimal to Octal?

To convert decimal to octal, repeatedly divide the decimal number by 8 and record each remainder. The octal result is the remainders read in reverse order (from last to first). For example: 255₁₀ ÷ 8 → remainders 7,7,3 → 377₈.

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.

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 corresponds exactly to a group of three binary digits, making octal a convenient intermediary between decimal and binary representations.

Decimal to Octal Conversion Table

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