Question

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

Multiplicand (\( M \))	Multiplier (\( Q \))
1100 1101 1110 1101	1010 0100 1010 1010

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

Hint:

Booth's multiplication algorithm reduces the number of addition/subtraction operations by encoding runs of 1s efficiently. The number of operations depends on the bit pattern of the multiplier.

Answer 1

Correct Answer: 13

Booth’s multiplication algorithm works by examining pairs of bits in the multiplier and deciding whether to add, subtract, or shift based on the pattern. The key steps include: - Scanning the bits of \( Q \) from right to left. - Performing addition when encountering a `01` transition. - Performing subtraction when encountering a `10` transition. - Shifting in all other cases. For the given numbers \( M = 1100 1101 1110 1101 \) and \( Q = 1010 0100 1010 1010 \), applying Booth’s algorithm results in 13 addition and subtraction operations.