4-Bit Johnson Counter: Lockup State Complete Analysis
Uninitialized flip-flops in hardware power up in unpredictable states, requiring robust recovery mechanisms.
The system is a standard 4-bit Johnson counter consisting of flip-flops Q0, Q1, Q2, and Q3. The shift direction is from left to right: D1 = Q0, D2 = Q1, and D3 = Q2. The inverted output of the final stage Q3' feeds back into the first stage D0.
Determine the next-state transitions for all states outside the standard 8-state valid sequence. Analyze the full invalid state graph and identify whether any of these power-on states naturally self-correct into the valid sequence without external reset logic.
Constraints
- Assume all flip-flops share a common clock and transition simultaneously.
- The state is represented as the 4-bit word
Q0 Q1 Q2 Q3. - The standard valid sequence begins at
0000.
Topics
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