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]
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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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