GATE | Gate IT 2008 | Question 40

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


Answer: (B)

Explanation: Booth’s algorithm: first take 2’s complement of given number if number is negative, then append 0 into LSB.

Then, for each pair from LSB to MSB (add 1 bit at a time):
00 = 0, 01 = +1, 10 = -1, 11 = 0

Booth’s algorithm is based on Multiplier which is already given in binary representation: 0111 0111 1011 1101

= Now, append 0 into LSB of (0111 0111 1011 1101) = 0111 0111 1011 1101 0
Now Booth's code (add 1 bit at a time, from LSB to MSB):
= 01, 11, 11, 10, 01, 11, 11, 11, 10, 01, 11, 11, 11, 10, 01, 10
= +1 0 0 -1 +1 0 0 0 -1 +1 0 0 0 -1 +1 -1

Therefore, 4 subtractions and 4 additions, total 8 additions/Subtractions are required.

So, option (B) is correct.

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