Counter: Adding Minimal Lockup Correction Gate
State machines in safety-critical systems must never remain trapped in unused states. When an existing mod-7 counter locks up at the invalid state 111, adding a targeted correction gate is far safer than rewriting all excitation equations.
The current next-state logic for the most significant bit is D2_current = Q2 AND Q1. This creates a self-loop at state 7 (Q2=1, Q1=1, Q0=1). Modify the logic to produce D2_corrected, ensuring the counter breaks out of state 7 while preserving the valid transition for state 6 (Q2=1, Q1=1, Q0=0).
| Q2 | Q1 | Q0 | D2_corrected | |------|------|------|----------------| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 |
Constraints
- Implement only the combinational logic for
D2_corrected. - Do not use sequential elements.
- Use the minimum number of basic logic gates.
Topics
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