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Booth multiplication of -6 × -11

Short answer

Booth's algorithm with 5-bit registers: -6 (11010) × -11 (10101), -M=00110. After five add/subtract and arithmetic right shifts, result in A,Q is 00010 00010 = 66.

Multiply -6 × -11 using Booth's multiplication algorithm.

Booth's algorithm with 5-bit registers (−6 = 11010, −11 = 10101).

Multiplicand M = -6 = 11010, multiplier Q = -11 = 10101, -M = 00110, n = 5 bits.

Step  Action               A      Q      Q-1
-     Initial              00000  10101  0
1     Q0Q-1=10: A = A - M  00110  10101  0
      ASR                  00011  01010  1
2     Q0Q-1=01: A = A + M  11101  01010  1
      ASR                  11110  10101  0
3     Q0Q-1=10: A = A - M  00100  10101  0
      ASR                  00010  01010  1
4     Q0Q-1=01: A = A + M  11100  01010  1
      ASR                  11110  00101  0
5     Q0Q-1=10: A = A - M  00100  00101  0
      ASR                  00010  00010  1

Result in A,Q = 00010 00010 = 66.

Answer: -6 × -11 = 66

✓ Answer checked by Claude Opus 5.5 (high effort)

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