Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $G(s)$ are given in the table. The value of the gain $K_I$ ($>0$) for a $50^\circ$ phase margin is _____ (rounded off to 2 decimal places).

Simplified form of the Boolean function

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

is

In the circuit, the present value of $Z$ is $1$. Neglecting the delay in the combinatorial circuit, the values of $S$ and $Z$, respectively, after the application of the clock will be

To obtain the Boolean function $F(X, Y) = X\overline{Y} + \overline{X}$, the inputs $PQRS$ in the figure should be