Mathematics
July 22, 2026 · 10 min read
Binary Multiplication: Shift-and-Add and Partial Products
Master binary multiplication with shift-and-add, partial products, and Booth's algorithm for signed numbers.
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Binary multiplication uses the shift-and-add method: multiply by each bit of the multiplier, shift left, and add partial products. The multiplication rules are simple: 0×0=0, 0×1=0, 1×0=0, 1×1=1.
Key Takeaway
Binary multiplication generates partial products and adds them. Hardware uses shift-and-add or array multiplier circuits.
1. The Process
- Multiply multiplicand by each bit of multiplier
- Shift each partial product left by its bit position
- Add all partial products
2. Booth\'s Algorithm
Booth\'s algorithm handles signed binary multiplication using two\'s complement. It examines pairs of bits and performs add, subtract, or shift operations based on the pattern.
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