Identifying a Johnson counter topology: Which name correctly describes a shift-register counter formed by feeding the inverted output of the last stage back to the first stage?

Introduction / Context:Counter topologies based on shift registers include the ring counter and the Johnson (twisted-ring) counter. Recognizing their feedback patterns helps predict sequence length, duty cycles, and decoding methods used in timing and control applications.

Given Data / Assumptions:

• The last stage output is inverted before being fed back to the first stage input.
• All stages clock simultaneously (synchronous shifting).
• Initialization places the register in a valid starting pattern.

Concept / Approach:In a simple ring counter, the last stage feeds back directly (non-inverted) to the first stage, causing a single 1 (or 0) to circulate and producing a modulus equal to the number of stages. In a Johnson counter, the inverted last-stage output is fed back to the first stage. This yields a sequence that is twice the number of stages in length (MOD = 2N), with patterns of consecutive 1s transitioning to consecutive 0s as the sequence progresses.

Step-by-Step Solution:

Verification / Alternative check:Draw a 4-stage example and simulate the shift: you will observe 8 distinct states before repeating, confirming the Johnson behavior and differentiating it from a 4-state simple ring counter.

Why Other Options Are Wrong:

Common Pitfalls:Confusing Johnson and ring counters due to similar schematics; overlooking the inversion bubble in feedback; assuming both have the same modulus.

Final Answer:Johnson counter