The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is

An equivalent 2’s complement representation of the 2’s complement number 1101 is

Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function.

The electric field vector of a wave is given as $$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}} \over {\sqrt {125} }}\,\,V/m$$$

Its frequency is 10 GHz.

(i) Investigate if this wave is a plane wave.
(ii) Determine its propagation constant, and
(iii) Calculate the phase velocity in $$y$$-direction.