Asynchronous (ripple) counter — interpreting stage #4's first toggle Four J–K flip-flops are cascaded as a ripple divider. When the output of the fourth stage toggles for the first time, how many input clock pulses have occurred at the counter input?

Introduction / Context:
Asynchronous (ripple) counters cascade toggling stages, each dividing the frequency of the previous stage by 2. Understanding the relationship between stage number and division factor enables quick reasoning about count values based on observed toggles at intermediate stages.

Given Data / Assumptions:

• Four J–K flip-flops configured to toggle (J = K = 1) in a ripple chain.
• Stage numbering: divider #1 sees the input clock; divider #4 is the fourth stage in the chain.
• Each stage divides by 2 relative to its input.

Concept / Approach:
Stage n in a ripple counter has output frequency f_in / 2^n and period 2^n input clock periods. A single transition (LOW→HIGH or HIGH→LOW) occurs every half-period of that stage, i.e., every 2^(n−1) input pulses. Therefore, the first toggle at stage #4 happens after 2^(4−1) = 8 input pulses.

Step-by-Step Solution:

Verification / Alternative check:
Think in binary count: after 8 input clocks, the 4-bit count is 1000₂, which corresponds to the MSB (stage #4) making its first transition from 0 to 1, matching the reasoning above.

Why Other Options Are Wrong:

• 16: that would be a full cycle of stage #4 (two toggles), not the first toggle.
• 4 or 2: correspond to stages #3 and #2, respectively.
• 1: is the toggle interval of stage #1 only.

Common Pitfalls:

• Confusing “toggle” (half-period) with “full period.” Stage #4’s period is 16 input pulses; its first toggle appears at 8.

Final Answer:
8