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Booth multiplication 7×3

Short answer

Booth's algorithm computes 7×3. M=0111, Q=0011, -M=1001, n=4. After 4 steps of add/subtract and arithmetic shift right, A,Q = 0001 0101 = 21. So 7 × 3 = 21.

Perform multiplication 7×3 using Booth algorithm.

Booth's algorithm: look at (Q0, Q-1); 10 means A = A − M, 01 means A = A + M, 00/11 mean no operation; then arithmetic shift right (ASR) of A, Q, Q-1. Repeat n times.

Multiplicand M = 7 = 0111, multiplier Q = 3 = 0011, -M = 1001, n = 4 bits.

Step  Action               A     Q     Q-1
-     Initial              0000  0011  0
1     Q0Q-1=10: A = A - M  1001  0011  0
      ASR                  1100  1001  1
2     Q0Q-1=11: no change  1100  1001  1
      ASR                  1110  0100  1
3     Q0Q-1=01: A = A + M  0101  0100  1
      ASR                  0010  1010  0
4     Q0Q-1=00: no change  0010  1010  0
      ASR                  0001  0101  0

Result in A,Q = 0001 0101 = 21.

Answer: 7 × 3 = 21

✓ Answer checked by Claude Opus 5.5 (high effort)

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