Consider a digital display system (DDS) shown in the figure that displays the contents of register X. A 16-bit code word is used to load a word in X, either from S or from R. S is a 1024-word memory segment and R is a 32-word register file. Based on the value of mode bit M, T selects an input word to load in X. P and Q interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of P, Q, and T?

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 $$\left( {0,0,1,1,2,2,3,3,0,0,...} \right)$$ is ____________.