Skip to content
Related Articles

Related Articles

Improve Article
GATE | Gate IT 2005 | Question 8
  • Last Updated : 29 Mar, 2018

Using Booth’s Algorithm for multiplication, the multiplier -57 will be recoded as
(A) 0 -1 0 0 1 0 0 -1
(B) 1 1 0 0 0 1 1 1
(C) 0 -1 0 0 1 0 0 0
(D) 0 1 0 0 -1 0 0 1


Answer: (A)

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

Therefore, given number in signed representation (2’s complementation) of -57

= 2's complement of (00111001) = 11000110+1 = 11000111
= append 0 into LSB of (11000111) = 110001110
Now Booth's code (add 1 bit at a time, from LSB to MSB):
= 11, 10, 00, 00, 01, 11, 11, 10 = 0 -1 0 0 1 0 0 -1

Alternative way –
You can calculated decimal values in given options:
(A) 0 -1 0 0 1 0 0 -1 = 0*(2^6) -1*(2^6) + 0*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 0*(2^1) -1*(2^0) = -2^6 + 2^3 – 2^0 = -64 +8 -1 = -57
(B) 1 1 0 0 0 1 1 1 = 2^7 + 2^6 + 2^2 2^1 + 2^0 = 199
(C) 0 -1 0 0 1 0 0 0 = -2^6 + 2^3 = -56
(D) 0 1 0 0 -1 0 0 1 = 2^6 – 2^3 + 2^0 = 57

So, option (A) is correct.

Quiz of this Question

Attention reader! Don’t stop learning now. Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :