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Booth multiplication of 6 × 7

Short answer

Using 4-bit Booth's algorithm, 6 (0110) × 7 (0111), -M=1010. The run of 1s requires one subtraction and one addition, giving final A,Q=0010 1010 = 42.

Multiply 6 × 7 using the Booth algorithm.

Booth's algorithm with 4-bit registers (6 = 0110, 7 = 0111). A run of 1s in the multiplier (0111) needs one subtraction at the start and one addition after the run.

Multiplicand M = 6 = 0110, multiplier Q = 7 = 0111, -M = 1010, n = 4 bits.

Step  Action               A     Q     Q-1
-     Initial              0000  0111  0
1     Q0Q-1=10: A = A - M  1010  0111  0
      ASR                  1101  0011  1
2     Q0Q-1=11: no change  1101  0011  1
      ASR                  1110  1001  1
3     Q0Q-1=11: no change  1110  1001  1
      ASR                  1111  0100  1
4     Q0Q-1=01: A = A + M  0101  0100  1
      ASR                  0010  1010  0

Result in A,Q = 0010 1010 = 42.

Answer: 6 × 7 = 42

✓ Answer checked by Claude Opus 5.5 (high effort)

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