The following two signed 2's complement numbers are being multiplied using Booth's algorithm:M: 1100

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Question

The following two signed 2's complement numbers are being multiplied using Booth's algorithm:M: 1100 1101 1110 1101 (multiplicand)Q: 1010 0100 1010 1010 (multiplier)The total number of addition and subtraction operations to be performed is ___________.

Accepted Answer

Answer: 13Concept — Booth's Algorithm: Scan multiplier Q right-to-left appending a guard bit (0). For each pair (Qᵢ, Qᵢ₋₁): 01 → +1 (add), 10 → −1 (subtract), 00 or 11 → no operation.Multiplier Q = 1010 0100 1010 1010, guard bit = 0:Pairs from right: (0,0)=0, (1,0)=−1, (0,1)=+1, (1,0)=−1, (0,1)=+1, (0,0)=0, (1,0)=−1, (0,1)=+1, (0,0)=0, (1,0)=−1, (0,1)=+1, (0,0)=0, (1,0)=−1, (0,1)=+1, (1,0)=−1, (1,1)=0Additions (+1): 6 times. Subtractions (−1): 7 times. Total = 6 + 7 = 13.

The following two signed 2's complement numbers are being multiplied using Booth's algorithm:M: 1100 1101 1110 1101 (multiplicand)Q: 1010 0100 1010 1010 (multiplier)The total number of addition and subtraction operations to be performed is ___________.

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The following two signed 2's complement numbers are being multiplied using Booth's algorithm:M: 1100 1101 1110 1101 (multiplicand)Q: 1010 0100 1010 1010 (multiplier)The total number of addition and subtraction operations to be performed is ___________.

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