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GATE EC|| DIGITAL LOGIC || BOOLEAN ALGEBRA || PYQS (2000-2025)
Question 1
The Boolean function A + BC is a reduced form of
(GATE 2014 || EC || MCQ ||1 MARK)
. AB + BC
(A + B). (A + C)
A̅B + ABC
(A + C).B
Question 2
The Boolean expression
(X + Y)(X + Y̅) + ((X Y̅)̅ + X̅)
Simplifies to
( GATE 2013 || EC || MCQ ||1 MARK )
X
Y
XY
X + Y
Question 3
In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals with 0V as logic 0 and Vcc as logic 1, the Boolean expression to Z is
(GATE 2013 || EC || MCQ ||1 MARK)
XY
[Tex]\overline{X}Y[/Tex]
[Tex]\overline{Y}X[/Tex]
[Tex]\overline{X}\overline{Y}[/Tex]
Question 4
If X = 1 in the logic equation
[ X + Z{ Y̅ + (Z̅ + XY̅) } ] [ X̅ + Z̅(X + Y) ] = 1, then
( GATE 2009 || EC || MCQ ||1 MARK)
Y = Z
Y = Z̅
Z = 1
Z = 0
Question 5
The Boolean expression for the truth table shown is
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |
(GATE 2005 || EC || MCQ ||2 MARK)
[Tex]B(A + C)(\overline{A} + \overline{C})[/Tex]
[Tex]B(A + \overline{C})(\overline{A} + C)[/Tex]
[Tex]\overline{B}(A + \overline{C})(\overline{A} + C)[/Tex]
[Tex]\overline{B}(A + C)(\overline{A} + \overline{C})[/Tex]
Question 6
The number of distinct Boolean expressions of 4 variables is
(GATE 2003 || EC || MCQ ||1 MARK)
16
256
1024
65536
Question 7
For the Boolean function F(A,B,C,D)=∑m(0,2,5,7,8,10,12,13,14,15) the essential prime implicants are
(GATE 2024 || EC || MCQ ||1 MARK)
BD + B̅D̅
BD + AB
AB + B̅D̅
BD + B̅D̅ + AB
Question 8
For the Boolean function
[Tex]F(A, B, C, D) = \sum m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15)[/Tex]
the essential prime implicants are _______.
( GATE 2024 || EC || MCQ ||1 MARK)
[Tex]BD, \bar{B} \bar{D}[/Tex]
[Tex]BD, AB[/Tex]
[Tex]AB, \bar{B} \bar{D}[/Tex]
[Tex]BD, \bar{B} \bar{D}, AB[/Tex]
Question 9
Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.
( GATE 2022 || EC || MSQ ||1 MARK)
X + Z + XY
(X +Y ) (X + Z)
X + XY + YZ
X + XZ + XY
There are 9 questions to complete.