Try it
Original
Step 1: flip every bit
Step 2: add 1 - two’s complement
Understand the result
What's going on
Computers don’t have a minus sign - everything is bits. Two’s complement is the trick that lets a fixed set of bits represent negative numbers too, using ordinary addition hardware with no special subtraction circuit needed.
The formula
two's complement = NOT(value) + 1
Show the derivation, mnemonic, and worked example
Build it up
Start from one’s complement - flip every bit - then add 1. That single extra step is what makes the arithmetic work out: adding a number to its two’s complement always produces all zeros (ignoring the overflow bit), which is exactly what you’d want from “a number plus its negative.” The top bit ends up doubling as a sign flag - 0 for positive, 1 for negative.
Worked example
Worked example
18 in 8-bit binary: 00010010
One's complement: 11101101
Two's complement: 11101110 (+1)
Read as signed 8-bit: −18 ✓
