GATE 2025 CS (CS2) – Question 32

Computer Organization and Architecture · Number Representation and Floating Point Arithmetic · 1 mark · Numerical answer

The following two signed 2's complement numbers (multiplicand M and multiplier Q) are being multiplied using Booth's algorithm:

M: 1100 1101 1110 1101 and Q: 1010 0100 1010 1010

The total number of addition and subtraction operations to be performed is ___________. (Answer in integer)

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Correct answer: 13

Explanation

Booth's algorithm performs one add/subtract for each adjacent bit pair $(Q_i, Q_{i-1})$ that differs, with $Q_{-1}=0$. For Q = 1010010010101010 followed by 0, there are 13 transitions, so 13 operations.