Figure shows a $$4$$ to $$1$$ $$MUX$$ to be used to implement the sum $$S$$ of a $$1$$-bit full adder with input bits $$P$$ and $$Q$$ and the carry input $${C_{in}}.$$ Which of the following combinations of inputs to $${{\rm I}_0},\,\,{{\rm I}_1},\,\,{{\rm I}_2}$$ and $$\,\,{{\rm I}_3}$$ of the $$MUX$$ will realize the sum $$S$$?

The Boolean expression $$X\overline Y Z + XYZ + \overline X Y\overline Z + \overline X \overline Y Z + XY\overline Z $$ can be simplified to

In the Fig. $${Z_1} = 10\angle - {60^ \circ },\,\,{Z_2} = 10\angle {60^ \circ },\,$$ $${Z_3} = 50\angle {53.13^ \circ }.\,\,$$ Thevenin's impedance seen from $$X-Y$$ is

The $$h$$ $$-$$ parameters for a two $$-$$ port network are defined by
$$\left[ {\matrix{ {{E_1}} \cr {{{\rm I}_2}} \cr } } \right] = \left[ {\matrix{ {{h_{11}}} & {{h_{12}}} \cr {{h_{21}}} & {{h_{22}}} \cr } } \right]\left[ {\matrix{ {{{\rm I}_1}} \cr {{E_2}} \cr } } \right].$$
For the two $$-$$ port network shown in Fig. the value of $${h_{12}}$$ is given by