Math
Binary to Decimal Converter
Convert any binary number to decimal, hex, and octal instantly.
In this article
How binary (base-2) works
Binary uses only 0s and 1s. Each position represents a power of 2: 1, 2, 4, 8, 16, 32...
Binary: 1 0 1 0
Value: 8 4 2 1 → 8+0+2+0 = 10 (decimal)
Why computers use binary
Transistors have two states: on (1) and off (0). Binary maps directly to this physical reality — making it the natural language of all digital computers.
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A single byte (8 bits) can represent 256 different values, which is why ASCII encoding contains 256 characters.
Frequently asked questions
How do I convert binary to decimal?▾
Multiply each digit by its place value (powers of 2, right to left) and add. 1011 = 8+0+2+1 = 11.
Why do computers use binary instead of decimal?▾
Transistors — the building blocks of processors — have two states: on (1) and off (0). Binary maps directly to these physical states. Building hardware with 10 distinct voltage levels (for decimal) would be far more complex, expensive, and error-prone.
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