GATE | GATE-CS-2016 (Set 2) | Question 17

Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _____________

[This Question was originally a Fill-in-the-blanks Question]

(A) -1
(B) 2
(C) 1
(D) -2

Answer: (A)


Here "longest latency for the sum to stabilize" means maximum delay that 
ripple carry adder would take to add A and B, we are given value of A and 
need to find the value of B.
The Delay in Ripple Carry Adder is as follows 
- For sum there are 2 XOR gates.
- For carry there is 1 XOR,1 AND and 1 OR gate.
i.e total 3 gate delays in case of carry and 2 gate delays in sum.
If we do 2's complement of 1 in 8 bit we get "00000001".
same we do for each option 
-1 : "11111111"
2 : "00000010"
1 : "00000001"
-2 : "11111110"

So in case of -1 the carry bit will change and thus it will take 1 extra
gate delay, hence we could see that the maximum delay we could get when
input at B will be -1, i.e. add “00000001” with “11111111” and would get Maximum delay.

This explanation has been provided by Harshit Sidhwa.

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