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Booth multiplication of 9 × -3

Short answer

M=9=01001, Q=-3=11101, -M=10111, 5 bits. Execute: 10 A−M, 01 A+M, 10 A−M, two steps no change, each with ASR. Result A,Q = 11111 00101 = -27.

Illustrate the multiplication of 9 and -3 using 2's complement method (Booth's algorithm).

Signed numbers are held in 2's complement form and Booth's algorithm handles the sign automatically (10 → A − M, 01 → A + M, then ASR). 5 bits are needed.

Multiplicand M = 9 = 01001, multiplier Q = -3 = 11101, -M = 10111, n = 5 bits.

Step  Action               A      Q      Q-1
-     Initial              00000  11101  0
1     Q0Q-1=10: A = A - M  10111  11101  0
      ASR                  11011  11110  1
2     Q0Q-1=01: A = A + M  00100  11110  1
      ASR                  00010  01111  0
3     Q0Q-1=10: A = A - M  11001  01111  0
      ASR                  11100  10111  1
4     Q0Q-1=11: no change  11100  10111  1
      ASR                  11110  01011  1
5     Q0Q-1=11: no change  11110  01011  1
      ASR                  11111  00101  1

Result in A,Q = 11111 00101 = -27.

Answer: 9 × -3 = -27

✓ Answer checked by Claude Opus 5.5 (high effort)

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