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:
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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.
The circuit is designed using 4 D-Flip-flops, which can theoretically represent \( 2^4 = 16 \) states. However, the number of distinct states before the circuit returns to the initial state depends on the feedback configuration.
In this type of sequential circuit, the number of distinct states can be found by examining the feedback connections, the state diagram, and the transitions between the states. If the circuit follows a typical binary counter with a feedback loop, it may only go through 7 unique states before returning to the initial state. This is because, in many cases, certain states are not reachable (due to the way the flip-flops are connected and the initial condition), leading to a smaller number of distinct states.
Thus, the circuit will go through 7 distinct states before returning to the initial state.
