BCD Counter: Power-On Invalid State Recovery Trace
A positive-edge-triggered BCD counter powers on in an invalid state, requiring the application of its minimized next-state logic to trace its recovery to a valid counting sequence.
Five signals are shown: CLK (clock, period 2), and four state outputs Q3, Q2, Q1, Q0 (initially 1, 1, 0, 1). The next-state logic equations for the flip-flops are: D3 = (Q3 & ~Q0) | (Q2 & Q0 & (Q1 | Q3)) D2 = Q2 ^ (Q1 & Q0) D1 = (Q1 ^ Q0) & (~Q3 | Q2) D0 = ~Q0
Trace outputs Q3, Q2, Q1, and Q0 across all 16 time steps.
Constraints
- Outputs update only on the LOW-to-HIGH transition of
CLK. - Standard bitwise operators are used:
~(NOT),&(AND),|(OR),^(XOR).
Topics
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