# Combinational Circuits

 Question 1
In the circuit shown below, $P$ and $Q$ are the inputs. The logical function realized by the circuit shown below is

 A $Y=P Q$ B $Y=P+Q$ C $Y=\overline{P Q}$ D $Y=\overline{P+Q}$
GATE EC 2023   Digital Circuits
Question 1 Explanation:
\begin{aligned} \text { Output } & =\bar{Q} \cdot I_{0}+Q \cdot I_{1} \\ & =\bar{Q} \cdot 0+Q \cdot P \\ & =P Q \end{aligned}
 Question 2
Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for $A_0,A_1,A_2 \text{ and }A_3$ are _______

 A $A_0=0,A_1=0,A_2=1,A_3=1$ B $A_0=1,A_1=0,A_2=1,A_3=0$ C $A_0=0,A_1=1,A_2=1,A_3=0$ D $A_0=1,A_1=1,A_2=0,A_3=0$
GATE EC 2022   Digital Circuits
Question 2 Explanation:

$f=\bar{C}\bar{D}I_0+\bar{C}DI_1+C\bar{D}I_2+CDI_3$
For this
$A_0=A_3=0$
$A_1=A_2=1$

 Question 3
The figure below shows a multiplexer where $S_1 \; and \; S_0$ are the select lines, $I_0 \; to \; I_3$ are the input data lines, EN is the enable line, and $F(P, Q, R)$ is the output, F is
 A $PQ+\bar{Q}R$ B $P+Q\bar{R}$ C $P\bar{Q}R+\bar{P}Q$ D $\bar{Q}+PR$
GATE EC 2020   Digital Circuits
Question 3 Explanation:
Output,$F=\bar{P}\bar{Q}R+P\bar{Q}R+PQ\, \, \, \,$
$F=\bar{Q}R+PQ$
 Question 4
A four-variable Boolean function is realized using 4x1 multiplexers as shown in the figure.
The minimized expression for F(U,V,W, X) is
 A $(UV+\bar{U}\bar{V})\bar{W}$ B $(UV+\bar{U}\bar{V})(\bar{W}\bar{X}+\bar{W}X)$ C $(U\bar{V}+\bar{U}V)\bar{W}$ D $(U\bar{V}+\bar{U}V)(\bar{W}\bar{X}+\bar{W}X)$
GATE EC 2018   Digital Circuits
Question 4 Explanation:

Output of the first multiplexer can be expressed as,
$F_{1}=\bar{U} V+U \bar{V}$
Output of the second multiplexer can be expressed as,
\begin{aligned} F &=\bar{W} \bar{X} F_{1}+\bar{W} X F_{1}=\bar{W} F_{1} \\ &=(\bar{U} V+U \bar{V}) \bar{W} \end{aligned}
 Question 5
A programmable logic array (PLA) is shown in the figure.

The Boolean function F implemented is
 A $\bar{P}\bar{Q}R + \bar{P}QR + P\bar{Q}\bar{R}$ B $(\bar{P}+\bar{Q}+R) (\bar{P}+Q+R) (P+\bar{Q}+\bar{R})$ C $\bar{P}\bar{Q}R + \bar{P}QR + P\bar{Q}R$ D $(\bar{P}+\bar{Q}+R) (\bar{P}+Q+R) (P+\bar{Q}+R)$
GATE EC 2017-SET-2   Digital Circuits
Question 5 Explanation:
$F=\bar{P} \bar{Q} R+\bar{P} Q R+P \bar{Q} R$

There are 5 questions to complete.