The two numbers given below are multiplied using the Booth's algorithm…
2009
The two numbers given below are multiplied using the Booth's algorithm Multiplicand: 0101 1010 1110 1110 Multiplier: 0111 0111 1011 1101 How many additions/subtractions are required for the multiplication of the above two numbers?
- A.
6
- B.
8
- C.
10
- D.
12
Attempted by 33 students.
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Correct answer: B
Booth's algorithm performs an addition or subtraction whenever there is a transition between consecutive bits in the multiplier sequence, including an implicit 0 appended at the LSB. By analyzing the given multiplier from LSB to MSB, we count the number of bit transitions (0→1 or 1→0). Each transition corresponds to one arithmetic operation. For the provided multiplier, there are exactly 8 transitions, meaning 8 additions or subtractions are required.