The following two signed 2’s complement numbers (multiplicand M and multiplier…

Final answer: 13 total operations (6 additions and 7 subtractions).

Reasoning:

• Booth's algorithm examines pairs (q_i, q_{i-1}) for i = 0..15 after appending q_{-1} = 0. If the pair is 01, add the multiplicand; if 10, subtract the multiplicand; if 00 or 11, do nothing.

• Write the multiplier bits from LSB to MSB and inspect each pair (q_i, q_{i-1}):

  1. i=0: (0, 0) -> no operation

  2. i=1: (1, 0) -> subtract

  3. i=2: (0, 1) -> add

  4. i=3: (1, 0) -> subtract

  5. i=4: (0, 1) -> add

  6. i=5: (1, 0) -> subtract

  7. i=6: (0, 1) -> add

  8. i=7: (1, 0) -> subtract

  9. i=8: (0, 1) -> add

  10. i=9: (0, 0) -> no operation

  11. i=10: (1, 0) -> subtract

  12. i=11: (0, 1) -> add

  13. i=12: (0, 0) -> no operation

  14. i=13: (1, 0) -> subtract

  15. i=14: (0, 1) -> add

  16. i=15: (1, 0) -> subtract

Count: additions = 6, subtractions = 7, total = 13.