Counter: Wrong Sequence Diagnosis
A 3-bit synchronous up-counter iterates through the binary sequence from 0 to 7 on each clock cycle. The next-state logic block computes the subsequent state D2, D1, D0 based on the current state Q2, Q1, Q0.
Expected behavior:
| Q2 | Q1 | Q0 | D2 | D1 | D0 | |------|------|------|------|------|------| | 0 | 0 | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 1 | 0 | 0 | 0 |
Simulation of the complete counter yields the sequence 0, 1, 2, 3, 5, 4, 7, 6, 0. The overall period is correct but the sequence is invalid. State 3 (Q2=0, Q1=1, Q0=1) incorrectly evaluates to next state 5 (D2=1, D1=0, D0=1) instead of 4 (D2=1, D1=0, D0=0). The least significant bit D0 evaluates incorrectly for this specific state transition.
Inspect the next-state logic circuit and correct the fault.
Constraints
- Do not alter the functional logic of
D2orD1which are evaluating correctly for state 3. - The final circuit must use standard logic gates to implement the correct excitation equations.
Topics
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