Counter taxonomy — ring and Johnson counters belong to which general class of counters when implemented with a common clock?

Introduction / Context:
Ring and Johnson (twisted-ring) counters are widely used to generate timing sequences and nonbinary state patterns. They are constructed from shift registers with feedback and clocked synchronously. This question asks which class they belong to under standard digital design classifications.

Given Data / Assumptions:

• Use of a shared clock for all stages.
• Feedback from serial output to serial input (inverted for Johnson).
• Focus on implementation style, not count radix.

Concept / Approach:
A counter is “synchronous” when all storage elements receive the same clock edge, and state changes occur simultaneously rather than rippling through successive devices. Ring and Johnson counters are built from synchronously clocked flip-flops that shift their content on each clock pulse; therefore, they are synchronous counters. They are not “true binary” counters because their state sequences are not binary-encoded numeric progressions; instead, they are one-hot (ring) or two-hot/overlapping (Johnson) patterns.

Step-by-Step Solution:

Verification / Alternative check:
Timing analysis shows no clock-to-clock ripple across flip-flops; outputs change together at the active edge, matching the synchronous definition.

Why Other Options Are Wrong:

• Asynchronous counters: imply ripple propagation, which ring/Johnson do not use.
• True binary counters: those count in binary coding (000... to 111...); ring/Johnson do not.
• Both asynchronous and true binary: incorrect on both counts.

Common Pitfalls:
Equating “counter” with “binary counter”; many counters are sequence generators rather than pure binary incrementers.

Final Answer:
Synchronous counters.