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Booth multiplication of 5 × -6

Short answer

M=5=0101, Q=-6=1010, -M=1011, 4 bits. Sequence: 00 no change, 10 A−M, 01 A+M, 10 A−M, each with ASR. Final A,Q = 1110 0010 = -30.

Multiply 5 and -6 using the Booth multiplication algorithm.

Booth's algorithm with 4-bit registers.

Multiplicand M = 5 = 0101, multiplier Q = -6 = 1010, -M = 1011, n = 4 bits.

Step  Action               A     Q     Q-1
-     Initial              0000  1010  0
1     Q0Q-1=00: no change  0000  1010  0
      ASR                  0000  0101  0
2     Q0Q-1=10: A = A - M  1011  0101  0
      ASR                  1101  1010  1
3     Q0Q-1=01: A = A + M  0010  1010  1
      ASR                  0001  0101  0
4     Q0Q-1=10: A = A - M  1100  0101  0
      ASR                  1110  0010  1

Result in A,Q = 1110 0010 = -30.

Answer: 5 × -6 = -30

✓ Answer checked by Claude Opus 5.5 (high effort)

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