AlgoPlus//structures / booths
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Booth's Multiplication

Signed multiply by examining bit pairs and arithmetic-shifting — add/subtract only at runs of bits.

Iteration
Action
Product
Legend
Examined bits (Q₀Q₋₁)
Multiplicand M
Accumulator A·Q
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In a nutshell
Booth's algorithm multiplies two signed numbers (positive or negative) using only the operations hardware already has: add, subtract, and shift. Instead of adding the multiplicand once for every 1 bit, it looks at pairs of bits to find where runs of 1s begin and end — subtracting once at the start of a run and adding once at the end. That lets it skip long stretches of identical bits, and it copes with negative numbers automatically.
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Booth’s multiplies signed numbers by reading bit pairs: a 0->1 transition subtracts the multiplicand, a 1->0 adds it, and runs of identical bits just shift. It handles sign directly and skips long bit-runs, so it is efficient on real operands.
Key terms
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