Asynchronous (ripple) down counter — intermediate transitional states An asynchronous 4-bit binary down counter changes from count 2 (0010₂) to count 3 (0011₂). How many intermediate transitional states (glitches) occur at the outputs during this change?

Introduction / Context:
Ripple counters change state sequentially as each flip-flop toggles in response to the previous stage, which can create transient intermediate states at the multi-bit output. Understanding when such glitches occur is important when driving decoders or combinational logic that might respond to the brief incorrect patterns.

Given Data / Assumptions:

• A 4-bit asynchronous (ripple) binary down counter.
• Transition considered: 2 (0010₂) → 3 (0011₂).
• Outputs observed directly at the counter pins.

Concept / Approach:
Transitional states occur when multiple bits need to change and do not toggle simultaneously. If only one bit changes for a given increment/decrement, then no intermediate invalid combination appears, because there is no propagation chain causing other stages to toggle during the event.

Step-by-Step Reasoning:

Verification / Alternative check:
Compare to a problematic boundary like 0000 → 1111 in a down counter (or 0111 → 1000 in an up counter), where multiple bits flip and glitches are expected. In contrast, 0010 → 0011 requires only one bit flip, so the transition is clean even in a ripple design.

Why Other Options Are Wrong:

• One/Two/Three: imply additional bits toggling, which does not occur for this specific transition.
• Fifteen: misinterprets “modulus” or assumes spurious oscillation.

Common Pitfalls:

• Assuming ripple counters always glitch; they glitch only when more than one bit changes.
• Confusing down vs. up transitions; the analysis hinges on which bits must toggle.

Final Answer:
None