Difficulty: Easy
Correct Answer: Incorrect
Explanation:
Introduction / Context:Frequency division chains are commonly made from toggle (T) flip-flops or JK/D flip-flops configured to toggle. Each stage divides the input frequency by 2. Understanding how many stages are required for a given divide ratio is fundamental.
Given Data / Assumptions:
Concept / Approach:To obtain divide-by-4, use 2 cascaded flip-flops: 2 * 2 = 4. Four flip-flops would yield divide-by-16, which is excessive for the stated goal. Therefore, the claim that it “takes four” is incorrect.
Step-by-Step Solution:
Stage 1: f_out1 = f_in / 2.Stage 2: f_out2 = f_out1 / 2 = f_in / 4.Thus only 2 flip-flops are needed for divide-by-4.Four flip-flops → f_in / 16 (divide-by-16), not /4.Verification / Alternative check:Build a small timing diagram for two cascaded T flip-flops; count edges to confirm the 4:1 ratio.
Why Other Options Are Wrong:
Correct: Would imply four stages are required; false.True only with JK or only with asynchronous clocks: Irrelevant; the divide-by-2 per stage holds for toggling stages regardless of style.Common Pitfalls:Confusing modulus with number of stages; assuming more stages are always needed; overlooking synchronous vs. ripple timing differences which affect phase/skew, not the divide ratio.
Final Answer:Incorrect
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