Ring Counter: Lockup State Analysis
Ring counters generate precise multiphase timing signals without decode logic by circulating a single active bit through a shift register. A standard 4-bit ring counter consists of four D flip-flops where the output of the last stage feeds directly back into the input of the first stage.
The state of the counter is defined by the bit pattern Q3 Q2 Q1 Q0. A valid operational sequence requires exactly one flip-flop to hold a 1 at any given time.
Analyze the state transitions for all sixteen possible 4-bit values. Determine the next-state behavior for non-standard initializations. Map the complete state transition diagram to identify all isolated cycles and permanent lockup conditions.
Constraints
- The counter is strictly positive-edge triggered.
- No self-correcting combinational logic is present in the feedback path.
- Shift direction is from
Q3down toQ0, withQ0feeding back intoQ3.
Topics
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