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Booth multiplication of -6 × 12

Short answer

Use 5-bit Booth: M=-6=11010, Q=12=01100. Sequence: 00 no change, 00 no change, 10 A=A−M, 11 no change, 01 A=A+M, each followed by ASR. Final A,Q = 11101 11000 = -72.

Multiply -6 × 12 using Booth's algorithm.

Use Booth's algorithm: 10 → A = A − M, 01 → A = A + M, 00/11 → no change, then ASR of A, Q, Q-1 for n cycles. Both numbers fit in 5 bits (−6 = 11010, 12 = 01100).

Multiplicand M = -6 = 11010, multiplier Q = 12 = 01100, -M = 00110, n = 5 bits.

Step  Action               A      Q      Q-1
-     Initial              00000  01100  0
1     Q0Q-1=00: no change  00000  01100  0
      ASR                  00000  00110  0
2     Q0Q-1=00: no change  00000  00110  0
      ASR                  00000  00011  0
3     Q0Q-1=10: A = A - M  00110  00011  0
      ASR                  00011  00001  1
4     Q0Q-1=11: no change  00011  00001  1
      ASR                  00001  10000  1
5     Q0Q-1=01: A = A + M  11011  10000  1
      ASR                  11101  11000  0

Result in A,Q = 11101 11000 = -72.

Answer: -6 × 12 = -72

✓ Answer checked by Claude Opus 5.5 (high effort)

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