GATE EC Combinatorial Circuits questions

In the figure shown, the output ܻ$Y = AB + \overline{C}\:\:\overline{D}$ is required to be ܻ The gates $G1$ and $G2$ must be, respectively,

A function of Boolean variables $X, Y$ and $Z$ is expressed in terms of the min-terms as $$F(X, Y, Z) = \Sigma (1, 2, 5, 6, 7)$$ Which one of the product of sums given below is equal to the function $F(X, Y, Z)?$

A $1$-to-$8$ demultiplexer with data input $D_{in}$ , address inputs $S_{0}, S_{1}, S_{2}$ (with $S_{0}$ as the LSB) and $\overline{Y_{0}}$ to $\overline{Y_{7}}$ as the eight demultiplexed outputs, is to be designed using two $2$-to-$4$ decoders (with enable input $\overline{E}$ and address inputs $A_{0}$ and $A_{1}$) as shown in the …

In the circuit shown, diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal, and the inputs $E_{1} , E_{2}$ and $E_{3}$ are $“0\: V”$ for logic $‘0’$ and $“10\: V”$ for logic $‘1’$. What logic gate does the circuit represent?

A universal logic gate can implement any Boolean function by connecting sufficient number of them appropriately. Three gates are shown. Which one of the following statements is TRUE?

The Boolean expression $(X+Y)(X+\overline{Y}) + \overline{(X\;\overline{Y}) + \overline{X}}$ simplifies to

The output $F$ in the digital logic circuit shown in the figure is

Consider the Boolean function $F(w,x,y,z) = wy + xy + \overline{w}\:xyz + \overline{w}\:\overline{x}\:y + xz + \overline{x}\:\overline{y}\:\overline{z}.$ Which one of the following is the complete set of essential prime implicants?

For an $n$-variable Boolean function, the maximum number of prime implicants is

In a half-subtractor circuit with $X$ and $Y$ as inputs, the Borrow $(M)$ and Difference $(N = X – Y)$ are given by

As FIR system is described by the system function $$H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{2}z^{-2}$$. The system is

Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit?

In the circuit shown, $W$ and $Y$ are MSBs of the control inputs. The output $F$ is given by

If $X$ and $Y$ are inputs and the Difference $(D=X-Y)$ and the Borrow $(B)$ are the outputs, which one of the following diagrams implements a half-subtractor?

A region shown below contains a perfect conducting half-space and air. The surface current $\overrightarrow{K_{s}}$ on the surface of the perfect conductor is $\overrightarrow{K_{s}}= \hat{x}2$ amperes per meter. The tangential $\overrightarrow{H}$ field in the air just above the perfect conductor is

In the circuit shown in the figure, if $C=0$, the expression for $Y$ is

The output $(Y)$ of the circuit shown in the figure is

An N-type semiconductor having uniform doping is biased as shown in the figure. If $E_C$ is the lowest energy level of the conduction band, $E_V$ is the highest energy level of the valance band and $E_F$ is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?

An $8$- to $1$ multiplexer is used to implement a logical function $Y$ as shown in the figure. The output $Y$ is given by

Two magnetically uncoupled inductive coils have $Q$ factors $q_{1}$ and $q_{2}$ at the chosen operating frequency. Their respective resistances are $R_{1}$ and $R_{2}.$ When connected in series, their effective $Q$ factor at the same operating frequency is