Two's Complement Arithmetic
Add signed numbers and watch for overflow.
Width
A = 00110010
B = 00011110
Σ = 01010000
Why it works
Negative numbers are stored as the two's complement: invert every bit, add 1. The most significant bit becomes the sign.
Addition uses the same binary adder as unsigned numbers — no special hardware for subtraction needed.
Overflow happens only when both operands share a sign and the result flips it. The carry into the sign bit differs from the carry out.