Considering ring counters versus Johnson (twisted-ring) counters, which statement correctly identifies a key structural difference between them?

Introduction / Context:
Ring and Johnson counters are shift-register based counters used for sequence generation and timing. While both circulate patterns through flip-flops, the way feedback is applied differentiates their state counts and decoding requirements. Recognizing the feedback type helps in choosing the right counter for a given number of states and ease of decoding.

Given Data / Assumptions:

• Ring counter: circulates a single 1 (one-hot) through N flip-flops.
• Johnson counter: feeds back the inverted output of the last flip-flop to the first.
• Both are clocked shift registers.

Concept / Approach:
A ring counter with N flip-flops provides N distinct one-hot states and generally needs minimal decoding but uses many flip-flops to get many states. A Johnson counter (twisted ring) with N flip-flops produces 2N unique states because the inverted feedback generates a two-phase pattern sequence. This can reduce decoding complexity for certain sequences and is the hallmark trait: inverted feedback path from the last stage to the first.

Step-by-Step Solution:
Ring: Q pattern 1000 → 0100 → 0010 → 0001 → 1000 (no inversion).Johnson: Q pattern evolves as 1111 → 1110 → ... → 0000 → 0001 → ... (due to inverted feedback).Count of states: Ring = N; Johnson = 2N.Conclusion: Johnson uses inverted feedback.

Verification / Alternative check:
Textbook timing diagrams and simulations show the twisted feedback for Johnson counters and the doubled state count relative to a simple ring, confirming the structural difference.

Why Other Options Are Wrong:

• Ring has inverted feedback: Incorrect; that defines Johnson, not ring.
• Flip-flop counts: Johnson achieves more states with the same flip-flops, not more flip-flops.
• Identical feedback: Contradicts the core distinction between the two.

Common Pitfalls:

• Confusing the one-hot nature of ring counters with Johnson sequences that feature consecutive ones and zeros.
• Assuming both have the same number of states per flip-flop; Johnson doubles the state count.

Final Answer:
a johnson counter has an inverted feedback path