Binary/Decimal/Hex/Octal Converter

Convert numbers between binary, decimal, hexadecimal, and octal instantly. Type in any field to see all conversions update in real time.

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How It Works

Every positional number system represents values using digits multiplied by powers of the base. In base b, the rightmost digit is multiplied by b⁰ = 1, the next by b¹, then b², and so on.

Binary (Base 2) uses only 0 and 1. It is the native language of computers — every bit in memory is a binary digit. For example, 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11₁₀.

Octal (Base 8) groups every 3 binary digits into one octal digit. Commonly used in Unix file permissions (e.g. 755 = rwxr-xr-x).

Hexadecimal (Base 16) groups every 4 binary digits into one hex digit. Widely used in programming for memory addresses, color codes (#FF0000), and byte values.

To convert between bases: the tool first converts the input to decimal (by summing digit × base^position), then converts from decimal to each target base (by repeated division, reading remainders in reverse).

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Quick Reference

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Common Use Cases

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