Consider the given sequential circuit designed using D-Flip-flops. The circuit…

Key idea: follow the state of the four flip-flops through successive clock cycles using the feedback connections shown in the diagram. Each clock updates Q0..Q3 according to the wires: each stage receives (from the previous stage) either the direct or complemented output as drawn, and the rightmost output is fed back to the leftmost input.

Trace one full cycle (starting from an example initial state) to count distinct states before the pattern repeats. For example, starting from the state 1000 (Q0=1, Q1=0, Q2=0, Q3=0) the circuit evolves as follows:

1. 1000 → after 1 clock → 0100

2. 0100 → after 2 clocks → 0010

3. 0010 → after 3 clocks → 0001

4. 0001 → after 4 clocks → 1110

5. 1110 → after 5 clocks → 0111

6. 0111 → after 6 clocks → 1011

7. 1011 → after 7 clocks → 1000 (back to the initial state)

Since we returned to the initial state after 7 distinct states, the circuit cycles through 7 distinct states before returning to the initial state. Therefore the answer is 7.