A Boolean function, $f(x, y, z)$ with $x$ as MSB and $z$ as LSB is realized by $4: 1$ multiplexer (MUX) with select lines, $S_1$ and $S_0$ ( $S_1$ is MSB, $S_0$ is LSB) and inputs, $I_0, I_1, I_2, I_3$ as shown in the Figure.

Which of the following options is the correct expression of $f(x, y, z)$ ?

A shift-left Shift Register (SR) and a $D$ flip-flop are connected to a synchronized clock as shown in the Figure. Assume that the SR and D flip-flops are initially cleared and the XOR gate has no propagation delay.

Which of the following options gives the correct binary representation $\left(b_7 b_6 b_5 b_4 b_3 b_2 b_1 b_0\right)$ of the content of the shift register immediately after the $5^{\text {th }}$ clock transition (positive edge)?

Consider the four-variable Boolean function, $f(w, x, y, z)=\Sigma m(0,2,5,7,8,10,13,14,15)$ with ' $w$ ' as MSB and ' $z$ ' as LSB. Which of the following expressions is/are the valid form(s) of $f(w, x, y, z)$ ?

Consider the Friis' transmission equation $P_R=\left(P_T G_T G_R \lambda^2\right) /(4 \pi D)^2$, where $P_R$ and $P_T$ are the received and the transmitted powers, respectively.

$G_T$ and $G_R$ are the gain of transmitting and receiving antennas, respectively, $D$ is the distance between the transmitting and receiving antennas, and $\lambda$ is the wavelength in free space.

Given: $G_T=G_R=1.0, \lambda=0.30 \mathrm{~m}$ and $P_T=+10 \mathrm{dBm}$.

Choose the distance (D), in km , from the following options at which the received power, $P_R=-90 \mathrm{dBm}$ ?