Unknown Counter: Reverse-Engineer from Excitation Equations
Reverse-engineering a counter from its excitation equations is a primary design review and debug technique. Hardware engineers frequently map raw Boolean logic back to state transition diagrams to verify safety and recovery mechanisms.
The circuit under review is a 3-bit synchronous counter with state variables Q2, Q1, and Q0. The next-state logic is defined by the following D-flip-flop excitation equations: D0 = Q1' D1 = Q0 XOR Q1 D2 = Q1·Q0 + Q2·Q1
Compute the complete 8-state next-state table. Trace the state transitions to identify the valid count cycle, find any invalid state paths, and determine if any states result in permanent lockup.
Constraints
- Assume standard positive-edge triggered D flip-flops.
- State values are represented as the integer value of the binary word
Q2 Q1 Q0, whereQ2is the most significant bit. Q1'represents the logical NOT ofQ1.
Topics
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Place the gates, wire them up and watch the signals settle. Every submission runs on the same simulation engine that grades it.
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