Computer Sciences > GATE 2025 SET-1 > Sequential Circuits
Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is ______ (Answer in integer)
Correct : 7
The correct answer is 7 (excluding the initial state) or 8 (including it).
For a D flip-flop, the characteristic equation is Qnext = D. From the circuit, the next-state equations are:
• Q0(next) = Q̅3
• Q1(next) = Q0
• Q2(next) = Q1
• Q3(next) = Q2
Starting from initial state 0000 and applying these equations at each clock cycle:
0000 → 0001 → 0011 → 0111 → 1110 → 1100 → 1000 → 0000
The circuit visits 7 distinct states (0001, 0011, 0111, 1110, 1100, 1000, and back to 0000) before returning to the initial state.
This is a classic Linear Feedback Shift Register (LFSR)-type circuit where Q̅3 feeds back to Q0, creating a cycle of length 7 (excluding the all-zero lock-up state).
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