Consider a circuit where X is the input and Y is the output, consisting of a NOT gate whose output f

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Question

Consider a circuit where X is the input and Y is the output, consisting of a NOT gate whose output feeds an AND gate along with X. Which of the following statements about the circuit is/are CORRECT?(A) With no propagation delays, the output Y is always logic Zero.(B) With no propagation delays, the output Y is always logic One.(C) With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One.(D) With propagation delays, the output Y can have a transient logic Zero after X transitions from logic One to logic Zero.

Accepted Answer

Correct Answer: (A) and (C)Concept -- Hazards in Combinational Circuits (from Morris Mano, Digital Design):The circuit computes Y = X AND (NOT X). This is a static-0 hazard circuit.(A) TRUE: Logically, Y = X AND (NOT X) = 0 for all values of X (by the complement law). With no propagation delays, both inputs of the AND gate are always complementary, so Y = 0 always.(B) FALSE: Y = X AND NOT(X) is always 0 logically, never always 1.(C) TRUE -- Static-1 Hazard: When X transitions from 0 to 1 with propagation delays: initially X=0, NOT(X)=1, Y = 0 AND 1 = 0. When X becomes 1 instantaneously but NOT(X) has not yet updated (still 1 due to gate delay), briefly Y = 1 AND 1 = 1 (a glitch). This is the classic static-0 hazard -- a transient 1 appears in a circuit whose steady-state output should be 0. Once NOT(X) updates to 0, Y returns to 0.(D) FALSE: When X transitions from 1 to 0: initially Y = 1 AND 0 = 0. As NOT(X) updates from 0 to 1 (delayed), the AND gate has inputs 0 (new X) and transitioning NOT(X). At no point does Y become 1 during this transition since X is already 0 and Y = 0 AND anything = 0. No transient 1 occurs in this direction.

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