Consider a relational database schema with a relation $R(A, B, C, D)$. If $\{A, B\}$ and $\{A, C\}$ are the only two candidate keys of the relation $R$, then the number of superkeys of relation $R$ is $\_\_\_\_$ . (answer in integer)

Consider the following Boolean expression of a function $F$ :

$$ F(P, Q)=(\bar{P}+Q) \oplus(\bar{P} Q) $$

Which of the following expressions is/are equivalent to $F$ ?

Consider the 8-bit signed integers $X, Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows:

$$ X: 10110100 \quad Y: 01001100 $$

Which of the following operations to compute $Z$ result(s) in an arithmetic overflow?

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 $D_0$ ?