Question

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:

 

Hint:

In sequential circuits, the number of distinct states is determined by the configuration of flip-flops and feedback connections. A common case involves a reduced number of states due to unreachable states.

Answer 1

Correct Answer: 7

Although four flip-flops are available, the sequence followed by the circuit is determined entirely by how the outputs are reused as inputs in the next clock cycle. Starting from the given initial condition, the circuit moves deterministically from one state to the next.

After a few clock pulses, the circuit reaches a state that has already occurred earlier in the sequence. From this point onward, the same pattern of states repeats cyclically.

Counting the number of unique states encountered before the first repetition shows that the circuit does not utilize all possible combinations. Only seven different states appear in the repeating cycle.

Hence, the circuit passes through \(\boxed{7}\) distinct states before returning to the initial state.