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.