A ripple counter is built from JK flip-flops with propagation delay t_pd = 12 ns, and is clocked at 10 MHz. What is the largest modulus (2^N) that can safely operate at this frequency?

Introduction / Context:Ripple counters cascade flip-flops so that the total propagation delay accumulates along the chain. The maximum clock frequency is constrained by the total worst-case delay through N stages.

Given Data / Assumptions:

• Flip-flop propagation delay t_pd = 12 ns.
• Clock frequency f_clk = 10 MHz → period T = 100 ns.
• Asynchronous (ripple) counter; worst-case path spans N stages.

Concept / Approach:

A common design rule for ripple counters is f_max ≈ 1 / (N * t_pd). The total delay must be less than the clock period to avoid incorrect counting.

Step-by-Step Solution:

Verification / Alternative check:

Timing simulation or STA (static timing analysis) will confirm that with N = 8, cumulative delay ≈ 96 ns, which fits within T = 100 ns margin.

Why Other Options Are Wrong:

• 16, 64, 128: smaller moduli than necessary; not the largest possible.
• 512: would require 9 stages → 9 * 12 ns = 108 ns > 100 ns, violating timing.

Common Pitfalls:

Using synchronous-counter timing limits (which are different); forgetting that ripple counters accumulate delays stage by stage.

Final Answer:

256