Signed binary to decimal converter
The same bits mean different numbers under different signed formats. This tool shows all four readings at once for computer organisation students.
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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
Sign-magnitude: the first bit is the sign and the rest is the size. One's complement: if the first bit is 1, the value is minus the inverted bits. Two's complement: the unsigned value minus 2 to the power n when the first bit is 1.
Example
Inputs: Binary number = 1011. Result: Sign-magnitude: -3.
1011
-3
Limits and caveats
- The leftmost bit is treated as the sign bit, so type the full width including leading zeros.
- A result of -0 is shown as is, since sign-magnitude and one's complement both have two zeros.
Questions about this tool
Why does 1011 give three different negatives?
Sign-magnitude reads 011 = 3, so -3. One's complement inverts to 0100, so -4. Two's complement gives 11 minus 16 = -5.
What does -0 mean?
Sign-magnitude and one's complement each have two zeros, such as 1000 and 1111 in 4 bits, one reason two's complement won out.
Which format do computers use for integers?
Two's complement on almost every common processor. Floating-point numbers use a sign-magnitude style sign bit.