GATE CS 2025 Set 2 — Question 32
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Computer Organization & Architecture → ALU & Datapath → Booth's Multiplication
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Question
The following two signed 2’s complement numbers (multiplicand M and multiplier Q) are being multiplied using Booth’s algorithm:
: 1100 1101 1110 1101 and : 1010 0100 1010 1010The total number of addition and subtraction operations to be performed is ___________. (Answer in integer)
: 1100 1101 1110 1101 and : 1010 0100 1010 1010The total number of addition and subtraction operations to be performed is ___________. (Answer in integer)
Correct answer
13 to 13
Solution
In Booth's multiplication algorithm, the number of addition and subtraction operations is determined by the number of transitions (0 to 1 or 1 to 0) in the multiplier bits , considering an implicit at the least significant end.The multiplier is given as .
Let's list the bits and append :Bits:
Implicit : We examine pairs for to :
Let's list the bits and append :Bits:
Implicit : We examine pairs for to :
- : Subtraction
- : Addition
- or : No arithmetic operation (only shift)
1.: No Op
2.: Subtraction (1)
3.: Addition (2)
4.: Subtraction (3)
5.: Addition (4)
6.: Subtraction (5)
7.: Addition (6)
8.: Subtraction (7)
9.: Addition (8)
10.: No Op
11.: Subtraction (9)
12.: Addition (10)
13.: No Op
14.: Subtraction (11)
15.: Addition (12)
16.: Subtraction (13)
Total operations = 13.Continue learning with Success Tracker
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