GATE CS 2024 Set 1 — Question 28
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Digital Logic → Combinational Circuits → Combinational Hazards
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Question
Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?
Correct answer
(A) With no propagation delays, the output Y is always logic Zero; (C) With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One
Solution
The circuit implements the Boolean function .
1.No propagation delays: In an ideal scenario without delays, the output is the logical product of a variable and its complement, which is always 0. Thus, for any value of . Statement (A) is correct.
2.With propagation delays: Let the propagation delay of the NOT gate be . The output of the AND gate at time is .
- Transition : Suppose changes from 0 to 1 at . For the interval , the direct input to the AND gate is 1, while the output of the NOT gate remains 1 because the change in hasn't propagated through it yet. Consequently, for a duration of . This is known as a transient logic One or a static-0 hazard. Statement (C) is correct.
- Transition : Suppose changes from 1 to 0 at . For , the direct input to the AND gate becomes 0 immediately, while the output of the NOT gate is still 0. Thus, . No transient occurs.
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