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Booth multiplication of 10 × (-5)

Short answer

Using Booth multiplication with 5-bit operands, process multiplier bit pairs and arithmetic-shift right after each add or subtract. For 10 times -5, the final A:Q is 1111001110, which equals -50.

Multiply 10 × (-5) using Booth's multiplication algorithm.

Booth's algorithm with 5-bit registers (10 = 01010, −5 = 11011).

Multiplicand M = 10 = 01010, multiplier Q = -5 = 11011, -M = 10110, n = 5 bits.

Step  Action               A      Q      Q-1
-     Initial              00000  11011  0
1     Q0Q-1=10: A = A - M  10110  11011  0
      ASR                  11011  01101  1
2     Q0Q-1=11: no change  11011  01101  1
      ASR                  11101  10110  1
3     Q0Q-1=01: A = A + M  00111  10110  1
      ASR                  00011  11011  0
4     Q0Q-1=10: A = A - M  11001  11011  0
      ASR                  11100  11101  1
5     Q0Q-1=11: no change  11100  11101  1
      ASR                  11110  01110  1

Result in A,Q = 11110 01110 = -50.

Answer: 10 × -5 = -50

✓ Answer checked by Claude Opus 5.5 (high effort)

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