Counter: K-Map Don't-Care Resolves to Lockup
State-machine lockup occurs when unmapped states resolve to self-looping conditions under power-on or noise events. A 3-bit mod-5 counter sequences through valid states 000 through 100. States 101 (5), 110 (6), and 111 (7) are initially treated as don't-cares during K-map minimization to simplify the logic.
The synthesized next-state logic for the most significant bit is given by the expression D2 = Q2 Q1 + Q2 Q0. The logic for the lower bits evaluates to D1 = 1 and D0 = 0 if the machine enters state 6 (110).
Trace the next-state evaluation for the unused states. Identify the K-map grouping that caused the hazard and determine the modification required to force a safe recovery.
Constraints
Q2is the most significant bit (MSB) andQ0is the least significant bit (LSB).- Valid states are
000through100. - States
101,110, and111are initially treated as don't-cares (X). - Assume standard sum-of-products boolean evaluation.
Topics
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