Binary to decimal converter
Type a binary number to get its decimal value at once, with the working shown step by step for computing and electronics students and programmers.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter binary number.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Multiply each digit by 2 raised to its position and add the results: power 0 for the rightmost whole digit, rising by 1 to the left, and -1, -2 after the point. Example: 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11.
Example
Inputs: Binary number = 101010. Result: Result in decimal: 42.
101010
42
Limits and caveats
- Negative numbers keep a minus sign in front of the magnitude; they are not shown in two's complement.
- Up to 2000 digits before the point and 200 after it.
Questions about this tool
How do I convert 1010 from binary to decimal?
Multiply each bit by its power of 2: 1×8 + 0×4 + 1×2 + 0×1 = 10.
Does it handle long numbers such as 64-bit values?
Yes. It uses exact integer arithmetic up to 2000 digits, so no digit is lost the way it can be on an ordinary calculator.
How are binary fractions like 0.101 worked out?
The first bit after the point is worth 1/2, the second 1/4 and the third 1/8, so 0.101 = 0.5 + 0.125 = 0.625.