# 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

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```

So, option (B) is correct.

Quiz of this Question

My Personal Notes arrow_drop_up

Article Tags :

1

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.