GATE CSE 2025 Session 2 Q32: Additions and subtractions in Booth's multiplication

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)

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 13 (official GATE 2025 final answer key)

Concept used: Booth's algorithm adds or subtracts M only when adjacent multiplier bits $(q_i, q_{i-1})$ differ.

First step: Append $q_{-1} = 0$ to Q and count the 01 and 10 transitions in 1010 0100 1010 1010 0.

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key