Consider the sequential circuit shown in the figure, where both flip-flops “$\text{FD A}$” and “$\text{FD B}$” used are positive edge-triggered $D$ flip-flops. The state of this circuit is represented by $(AB).$
This circuit is a $2$-bit complex counter with one input $x$ and depending on the value of $x,$ it gives a different counting sequence.
$D_{A}$ and $D_{B}$ are functions of variables $A, B, x$. Which of the following is true for $D_{A}(A, B, x)$ and $D_{B}(A, B, x)$ ? (PI means prime implicant and EPI means Essential Prime implicant)
- Number of PI for $D_{A}$ is $3$ and Number of EPI for $D_{B}$ is $2.$
- Number of PI for $D_{A}$ is $3$ and Number of EPI for $D_{B}$ is $3.$
- Number of PI for $D_{A}$ is $2$ and Number of EPI for $D_{B}$ is $2.$
- Number of PI for $D_{A}$ is $2$ and Number of EPI for $D_{B}$ is $3.$
