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Booth multiplication of -7 × -10

Short answer

In Booth multiplication, add or subtract the multiplicand based on multiplier bit pair Q0,Q-1 and arithmetic-shift right each cycle. For -7 times -10, the final A:Q is 0001000110, which equals 70.

Multiply -7 × -10 using Booth's multiplication algorithm.

Booth's algorithm with 5-bit registers (−7 = 11001, −10 = 10110).

Multiplicand M = -7 = 11001, multiplier Q = -10 = 10110, -M = 00111, n = 5 bits.

Step  Action               A      Q      Q-1
-     Initial              00000  10110  0
1     Q0Q-1=00: no change  00000  10110  0
      ASR                  00000  01011  0
2     Q0Q-1=10: A = A - M  00111  01011  0
      ASR                  00011  10101  1
3     Q0Q-1=11: no change  00011  10101  1
      ASR                  00001  11010  1
4     Q0Q-1=01: A = A + M  11010  11010  1
      ASR                  11101  01101  0
5     Q0Q-1=10: A = A - M  00100  01101  0
      ASR                  00010  00110  1

Result in A,Q = 00010 00110 = 70.

Answer: -7 × -10 = 70

✓ Answer checked by Claude Opus 5.5 (high effort)

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