Sequential Circuits

Consider a finite state machine (FSM) with one input $X$ and one output $f$, represented by the given state transition table. The minimum number of states required to realize this FSM is ________. (Answer in integer) $$\begin{array}{|c|cc|cc|} \hline \text{Present state} & \text{Next state } (X = 0) & \text{Next state } (X = 1) & \text{Output } f\ (X = 0) & \text{Output } f\ (X = 1) \\ \hline A & F & B & 0 & 0 \\ B & D & C & 0 & 0 \\ C & F & E & 0 & 0 \\ D & G & A & 1 & 0 \\ E & D & C & 0 & 0 \\ F & F & B & 1 & 1 \\ G & G & H & 0 & 1 \\ H & G & A & 1 & 0 \\ \hline \end{array}$$

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)

In a 4-bit ripple counter, if the period of the waveform at the last flip-flop is 64 microseconds, then the frequency of the ripple counter in kHz is ________. (Answer in integer)

Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops. The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of "in" is _____.

We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is ________.

The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0,0,1,1,2,2,3,3,0,0,…) is _____.