purr.tools

Binary to Decimal Converter

Enter a binary number to convert to decimal, hexadecimal, and octal — or enter a decimal number to convert to binary.

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How to convert binary to decimal

Each binary digit (bit) represents a power of 2. Starting from the rightmost bit (position 0), multiply each digit by 2 raised to its position, then sum the results. For example: 1010 = 1x8 + 0x4 + 1x2 + 0x1 = 10. You can also type a decimal number and the tool converts it to binary.

Number base reference

Binary (base 2) uses digits 0 and 1. Decimal (base 10) uses digits 0-9. Hexadecimal (base 16) uses digits 0-9 and A-F. Octal (base 8) uses digits 0-7. Common binary values: 0000=0, 0001=1, 0010=2, 0100=4, 1000=8, 1111=15, 11111111=255.

FAQ

Why is binary used in computers?

Computer hardware uses transistors that are either on (1) or off (0). Binary maps directly to this two-state physical reality. All data — numbers, text, images, code — is ultimately stored and processed as sequences of binary digits.

What is hexadecimal used for?

Hexadecimal is a compact way to represent binary. Each hex digit represents exactly 4 bits. A byte (8 bits) is two hex digits — for example, 255 in decimal = FF in hex = 11111111 in binary. Hex is widely used in memory addresses, color codes, and debugging.

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  src="https://purr.tools/en/embed/binary-to-decimal"
  width="100%"
  height="500"
  style="border:0;border-radius:8px;"
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  title="Binary to Decimal Converter — Free Online Tool"
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