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.

Inpur	Current state		Next state
$$ P $$	$$ Q_1 $$	$$ Q_0 $$	$$ Q_1^{+} $$	$$ Q_0^{+} $$
$$ \begin{aligned} & 0 \\ & 0 \\ & 0 \\ & 0 \\ & 1 \\ & 1 \\ & 1 \\ & 1 \end{aligned} $$	$$ \begin{aligned} & 0 \\ & 0 \\ & 1 \\ & 1 \\ & 0 \\ & 0 \\ & 1 \\ & 1 \end{aligned} $$	$$ \begin{aligned} & 0 \\ & 1 \\ & 0 \\ & 1 \\ & 0 \\ & 1 \\ & 0 \\ & 1 \end{aligned} $$	$$ \begin{aligned} & 0 \\ & 1 \\ & 1 \\ & 1 \\ & 0 \\ & 0 \\ & 0 \\ & 1 \end{aligned} $$	$$ \begin{aligned} & 1 \\ & 0 \\ & 1 \\ & 1 \\ & 0 \\ & 0 \\ & 1 \\ & 0 \end{aligned} $$

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

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)

Consider a sequential digital circuit consisting of T flip-flops and D flip-flops as shown in the figure. CLKIN is the clock input to the circuit. At the beginning, Q1, Q2 and Q3 have values 0, 1 and 1, respectively.

Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this digital circuit?

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?