If the multiplier Q is 1101 (-3 in decimal) and 4 bit registers are in use,…
2026
If the multiplier Q is 1101 (-3 in decimal) and 4 bit registers are in use, then in Booth's technique for multiplication the number of addition and subtractions required are:
- A.
1 addition and 2 subtractions
- B.
2 additions and 1 subtraction
- C.
1 addition and 1 subtraction
- D.
0 addition and 2 subtractions
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Correct answer: A
For Q = 1101 and initial Q₋₁ = 0, examine adjacent Booth pairs from LSB to MSB: (Q₀,Q₋₁)=10, (Q₁,Q₀)=01, (Q₂,Q₁)=10, (Q₃,Q₂)=11. The operations are subtraction, addition, subtraction and no operation. Therefore Booth's technique requires 1 addition and 2 subtractions. Hence, Option A is correct.