Frequency division with toggle flip-flops: “It takes four flip-flops to build a divide-by-4 frequency divider.” Evaluate the statement.

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:

• Each toggling flip-flop divides frequency by 2.
• Divide ratio of a cascade equals the product of stage ratios.
• No special gating or modulus changes are used.

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:

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:

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