Counter: Two Separate Invalid State Cycles
Robust digital systems must recover gracefully from random power-on states or radiation-induced bit flips.
A synchronous 4-bit counter uses state variables Q3, Q2, Q1, and Q0 to implement a standard BCD decade sequence from 0 to 9. The next-state logic produces the valid sequence perfectly, but the unused states (10 through 15) exhibit unintended transition behavior. The transition logic dictates the following mappings for the invalid states: 10 transitions to 12, 12 transitions to 14, 14 transitions to 10, 11 transitions to 13, 13 transitions to 15, and 15 transitions to 11.
Analyze the state transition behavior for all 16 possible states. Determine the topology of the unused states and identify the necessary logic to guarantee self-correction to the valid sequence.
Constraints
- Valid states are 0 (
0000) through 9 (1001). - State variables are ordered
Q3(MSB) down toQ0(LSB). - States 10 through 15 are considered invalid.
Topics
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