GATEverse — GATE CSE previous year questions

Consider a $2$ -bit saturating up/down counter that performs the saturating up count when the input $P$ is $0$ , and the saturating down count when $P$ is $1$ . The Next State table of the counter is as shown. The counter is built as a synchronous sequential circuit using D flip-flops. InputCureent StateNext State $\text{P}$$\text{Q}_{1}$$\text{Q}_{0}$$\text{Q}_{1}^{+}$$\text{Q}_{0}^{+}$ $0$$0$$0$$0$$1$ $0$$0$$1$$1$$0$ $0$$1$$0$$1$$1$ $0$$1$$1$$1$$1$ $1$$0$$0$$0$$0$ $1$$0$$1$$0$$0$ $1$$1$$0$$0$$1$ $1$$1$$1$$1$$0$ Which one of the following options corresponds to the expressions for the inputs of the D flip-flops, $D_{1}$ and $D_{0}$ ?

(A)

$D_{1}=P Q_{1}+\bar{P} Q_{0}+Q_{1} Q_{0} \quad D_{0}=P Q_{0}+\bar{P} Q_{1}+Q_{1} \overline{Q_{0}}$

(B)

$D_{1}=\bar{P} Q_{1}+\bar{P} Q_{0}+Q_{1} Q_{0} \quad D_{0}=\bar{P} \overline{Q_{0}}+\bar{P} Q_{1}+Q_{1} \overline{Q_{0}}$

(C)

$D_{1}=\bar{P} \overline{Q_{1}}+\bar{P} Q_{0}+Q_{1} Q_{0} \quad D_{0}=\bar{P} Q_{0}+\bar{P} Q_{1}+Q_{1} \overline{Q_{0}}$

(D)

$D_{1}=P \overline{Q_{1}}+\bar{P} Q_{0}+Q_{1} Q_{0} \quad D_{0}=P \overline{Q_{0}}+\bar{P} Q_{1}+Q_{1} \overline{Q_{0}}$