Two's Complement Calculator (Signed Binary)

Convert a signed number to two’s complement, or read a bit pattern as signed and unsigned.

By TheCalcTools Updated October 17, 2026 Formula checked and tested

Your numbers

Convert

Signed decimal

Binary pattern

Width

Binary (two's complement)

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Hexadecimal

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Signed value

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Unsigned value

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Range for this width

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Two’s complement stores negative numbers as 2^width minus the magnitude, so the top bit acts as a sign. −42 in 8 bits is 256 − 42 = 214 = 11010110.

To negate a number by hand, flip all bits and add 1. The binary and hex shown include a leading 1 that marks the width; read the digits after it.

Pattern = value mod 2^width; signed = pattern − 2^width if the top bit is 1

Using the default values shown in the calculator:

Convert	Signed decimal to two’s complement
Signed decimal	-42
Binary pattern	11010110
Width	8-bit

Result:

Why two's complement?

Addition and subtraction work the same for signed and unsigned numbers, and there is only one zero.

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.