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Booth multiplication of -5 × -9

Short answer

M=-5=11011, Q=-9=10111, -M=00101, 5 bits. Steps: 10→A−M, 11→no change, 11→no change, 01→A+M, 10→A−M, with ASR after each. Result A,Q = 00001 01101 = 45.

Multiply -5 × -9 using Booth's multiplication algorithm.

Booth's rule: 10 → A = A − M, 01 → A = A + M, 00/11 → no change; then ASR of A, Q, Q-1. Five bits are needed for the signed numbers.

Multiplicand M = -5 = 11011, multiplier Q = -9 = 10111, -M = 00101, n = 5 bits.

Step  Action               A      Q      Q-1
-     Initial              00000  10111  0
1     Q0Q-1=10: A = A - M  00101  10111  0
      ASR                  00010  11011  1
2     Q0Q-1=11: no change  00010  11011  1
      ASR                  00001  01101  1
3     Q0Q-1=11: no change  00001  01101  1
      ASR                  00000  10110  1
4     Q0Q-1=01: A = A + M  11011  10110  1
      ASR                  11101  11011  0
5     Q0Q-1=10: A = A - M  00010  11011  0
      ASR                  00001  01101  1

Result in A,Q = 00001 01101 = 45.

Answer: -5 × -9 = 45

✓ Answer checked by Claude Opus 5.5 (high effort)

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