Two-bit ripple counter — state after four clock pulses Two JK flip-flops are cascaded as a ripple counter with J = K = 1 on both stages (divide-by-4 counter). Starting from 00, what is the binary state after four input clock pulses?

Introduction / Context:
Cascading JK flip-flops with J = K = 1 creates a toggle chain in which each stage divides the previous stage’s frequency by 2. Two such stages form a 2-bit ripple counter that cycles through four states (00 → 01 → 10 → 11 → 00 …).

Given Data / Assumptions:

• Two stages, asynchronous ripple configuration.
• Each stage toggles on the appropriate clock edge when its input stage toggles.
• Initial state is 00 (Q1Q0).

Concept / Approach:
A 2-bit counter has a modulus of 4. After exactly four input clock pulses, the counter completes one full cycle and returns to its initial state. Therefore, the state after four pulses is 00 again.

Step-by-Step Solution:

Verification / Alternative check:
Think in modulo arithmetic: count value N advances by 1 each pulse modulo 4. After 4 increments, N ≡ 0 (mod 4), which maps back to 00.

Why Other Options Are Wrong:

• 01, 10, 11: these are intermediate states after 1, 2, or 3 pulses, not after 4.
• 11 (with carry): not applicable; the 2-bit counter simply wraps to 00.

Common Pitfalls:

• Starting from an assumed state other than 00; the answer is contingent on the initial condition.

Final Answer:
00