Asynchronous binary down counter — On each active clock pulse, what happens to the parallel output word (i.e., the binary count present across all flip-flop outputs) of an asynchronous DOWN counter?

Introduction:
An asynchronous (ripple) down counter is a fundamental digital circuit used to count downward in binary. Understanding how the parallel output word changes with each clock pulse is essential for timing, division, and event counting applications.

Given Data / Assumptions:

• The counter is configured as a binary DOWN counter.
• Flip-flops are arranged in ripple fashion (output of one feeds the clock of the next).
• Each valid clock pulse triggers one count event.
• No asynchronous clears/loads occur during counting.

Concept / Approach:

In a down counter, the least significant bit toggles every clock, and higher bits toggle on the appropriate transitions of lower bits. Regardless of internal propagation delays, the ideal net effect per external clock event is that the overall binary number represented by the parallel outputs steps down by one count (modulo the counter length).

Step-by-Step Solution:

Verification / Alternative check:

Simulate a 4-bit ripple down counter: 0000 underflows to 1111, then 1110, 1101,… Each clock decrements the binary value by one, confirming the rule independently of transient glitches.

Why Other Options Are Wrong:

• Decreases by 2: That would require two toggles per clock or a different modulus.
• Increases by 1/2: Describes up counting, not down counting.
• Toggles randomly: Ripple propagation causes momentary glitches, not random final values.

Common Pitfalls:

• Observing intermediate ripple states and misinterpreting them as final counts.
• Forgetting modulus wraparound at 000…0.

Final Answer:

The output word decreases by 1.