Converting an asynchronous up-counter to a down-counter For a ripple (asynchronous) binary counter built from leading edge-triggered flip-flops, which change produces decrementing behavior?

Introduction / Context:
Ripple counters propagate a derived clock from one flip-flop to the next. Whether the counter counts up or down depends on which output (Q or Q̅) is used to clock subsequent stages and on the triggering edge.

Given Data / Assumptions:

• Each stage is edge-triggered on the same edge type.
• The first stage is clocked by the external clock source.
• Subsequent stages are clocked by outputs of the preceding stage.

Concept / Approach:
In a binary ripple up-counter, each next stage is typically clocked from the Q output of the previous stage. To reverse the count direction, clock each next stage from the complementary output Q̅ (the “other side”), which inverts the sequencing, producing a down-count. Simply changing the sampling edge or taking the final readout from Q̅ does not universally implement a proper down-count in the typical configuration.

Step-by-Step Solution:

Verification / Alternative check:
Simulate a 3-bit counter and compare Q2 Q1 Q0 sequences for the two chaining methods; the Q̅-chained design walks the binary states in reverse order.

Why Other Options Are Wrong:
Taking the output from the other side for display (option a) doesn’t change the internal chaining. Changing to trailing-edge devices (option c) without re-chaining does not guarantee reverse counting. “All of the above” is therefore incorrect.

Common Pitfalls:
Forgetting that ripple counters are sensitive to propagation delays; re-chaining must still satisfy timing and fanout limits.

Final Answer:
clocking of each succeeding flip-flop from the other side ( instead of Q)