Don't-Care Self-Loop Audit: Post-Optimization Check
K-map minimization assigns don't-care next-states based on coverage optimization rather than self-correction. The resulting logic equations can inadvertently produce self-loops at these don't-care states, requiring a mandatory post-minimization audit.
A mod-6 counter uses three flip-flops with state variables Q2, Q1, and Q0 from most to least significant bit. States 6 (110) and 7 (111) are treated as don't-cares during logic minimization. The resulting optimized D excitation equations are:
D2 = Q2Q1' + Q1Q0 D1 = Q2'Q0 + Q1Q0' D0 = Q1'
Compute the next-state values for the unused states. Determine if the minimized equations produce any self-loops and verify if the counter is safe from lockup.
Constraints
- State variables are ordered
Q2,Q1,Q0. - Provide binary answers as 3-bit strings without spaces.
- Next-state evaluation assumes ideal, zero-delay flip-flops.
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.
This problem is part of Codiode Pro. The statement above is free to read.
The circuit builder and code editor need a desktop screen. On a phone, read the problem here and open it on a laptop to solve.