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. Which one of the following options corresponds to the expressions for the inputs of the D flip-flops, $D_1$ and $D_0$?

For a D flip-flop, the excitation equation is $D = Q^+$.

From the given Next State table for inputs $(P, Q_1, Q_0)$:

1. For flip-flop $D_1 = Q_1^+$:

   • Minterms where $Q_1^+ = 1$: $m(1, 2, 3, 7)$

   • Grouping on a 3-variable K-map:

     • Group 1 ($m_1, m_3$): $\overline{P} Q_0$

     • Group 2 ($m_2, m_3$): $\overline{P} Q_1$

     • Group 3 ($m_3, m_7$): $Q_1 Q_0$

   • Therefore, $$D_1 = \overline{P} Q_1 + \overline{P} Q_0 + Q_1 Q_0$$

2. For flip-flop $D_0 = Q_0^+$:

   • Minterms where $Q_0^+ = 1$: $m(0, 2, 3, 6)$

   • Grouping on a 3-variable K-map:

     • Group 1 ($m_0, m_2$): $\overline{P}\,\overline{Q_0}$

     • Group 2 ($m_2, m_3$): $\overline{P} Q_1$

     • Group 3 ($m_2, m_6$): $Q_1 \overline{Q_0}$

   • Therefore, $$D_0 = \overline{P}\,\overline{Q_0} + \overline{P} Q_1 + Q_1 \overline{Q_0}$$

Hence, option (B) is the correct choice.