Johnson counter fundamentals In a 4-bit Johnson (twisted-ring) counter, how many distinct states (bit patterns) occur in one full sequence?

Introduction / Context:Johnson counters are popular for generating multiple evenly spaced timing phases with minimal decoding. Knowing the number of states helps size the counter for a desired number of phases.

Given Data / Assumptions:

• Counter type: 4-bit Johnson counter.
• Feedback is inverted (twisted ring).

Concept / Approach:An n-bit Johnson counter cycles through 2n unique states. For n = 4, that is 8 distinct patterns, doubling what a regular ring counter would produce with the same number of flip-flops.

Step-by-Step Solution:

Verification / Alternative check:Enumerating the sequence shows the output walks through eight unique nonoverlapping patterns before repeating, used commonly to create 8-phase timing signals from four flip-flops.

Why Other Options Are Wrong:

• 1 or 2: Far too small; even a fixed or toggle state machine exceeds these counts.
• 4: This would be the count for a 4-stage ring (not twisted) counter, not a Johnson counter.

Common Pitfalls:

• Confusing Johnson with simple ring counters.
• Assuming 2^n states as in a binary counter; Johnson uses 2n states.

Final Answer:8