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Binary to Decimal Converter

Type a binary number and see its decimal value — plus the full step-by-step working.

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How the Binary to Decimal Converter Works

Binary is a base-2 system: every digit is a bit, 0 or 1, and each position is worth a power of 2. Starting from the right, the positions are worth 1, 2, 4, 8, 16, and so on. To convert, multiply each bit by its position value and add the results.

Example: 1011 in binary. From the right: 1 × 1 = 1, 1 × 2 = 2, 0 × 4 = 0, 1 × 8 = 8. Add them: 1 + 2 + 0 + 8 = 11. So 1011 in binary equals 11 in decimal. The converter below shows exactly this working for any binary number you enter.

Computers use binary because their circuits have two states — on and off — which map naturally to 1 and 0. That is why programmers, students, and electronics hobbyists convert between binary and decimal so often.

Frequently Asked Questions

How do I convert binary to decimal by hand?
Write the binary number, label each bit from the right starting at 0, multiply each bit by 2 raised to its position, and add all the products. For 1011: 1×8 + 0×4 + 1×2 + 1×1 = 11.
What is 1011 in decimal?
1011 in binary equals 11 in decimal: 1×8 + 0×4 + 1×2 + 1×1 = 11.
Can I convert binary fractions?
Yes, with negative powers of 2 after the point: in 101.1, the .1 means 1×2^-1 = 0.5, so the value is 5.5. This converter handles whole binary numbers; the same rule extends to fractions.
Why do computers use binary?
Computer circuits have two stable states, on and off, which map directly to the digits 1 and 0. Binary is therefore the natural language of computer hardware.

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