4-Bit Custom Counter: Complete State Transition Diagram
Complete state transition diagrams are the definitive tool for verifying counter correctness in silicon. They reveal all lockup states, recovery paths, and cycle lengths in a single view.
The circuit below is a custom 4-bit synchronous counter using D flip-flops. The state vector is defined as Q3 Q2 Q1 Q0. The excitation equations for the next state logic are:
D3 = Q2 D2 = Q1 D1 = Q0 D0 = Q3' Q2'
The intended valid count sequence begins at state 0000.
Compute the next state for all 16 possible configurations. Map the complete directed graph of state transitions. Identify the length of the valid cycle, locate any invalid state cycles, and determine if uninitialized states safely recover.
Constraints
- All flip-flops are synchronous and share the same positive-edge-triggered clock.
- The notation
Q3'indicates the logical NOT of signalQ3. - State values in text questions should be provided in binary format (e.g.,
0101) unless decimal is explicitly requested.
Topics
Solve this problem
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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