A 'code converter' is to be designed to convert from the BCD(5421) to the normal BCD (8421). The input BCD combinations for each digit are below. A block diagram of the converter is shown in figure.
(A) draw K-map for outputs, W, X, Y, and Z.
(B) Obtain minimized expression for the outputs W, X, Y, and Z.

Two dipoles are so fed and oriented in free space that they produce the following electromagnetic waves: $$${E_x} = 10\,{e^{j\left( {\omega t - z\pi /3} \right)}}\,\,volts/metre$$$ $$${E_y} = j\,\,10\,{e^{j\left( {\omega t - z\pi /3} \right)}}\,\,volts/metre$$$

(a) Write down the expression for the corresponding magnetic field strength vector.
(b) Calculate the frequency of the wave.
(C) Give the complete description of the polarization of the wave.

A rectangular hollow metal waveguide is required to be so designed to propagate a 9375 MHz signal in its $$T{E_{10}}$$-mode that the guide-wavelength equals the cut-off wavelength. Calculate the value of 'a' (breadth or the wider dimension of the waveguide). Take b = a/2. Also, calculate the cut-off frequency of the next higher order mode.

In the infinite plane, y = 6 m, there exists a uniform surface charge density of (1/6000$$\pi $$) $$\mu $$C/m². The associated electric field strength is: