1
GATE CSE 2018
Numerical
+2
-0
Consider the minterm list form of a Boolean function 𝐹 given below. $$F\left( {P,Q,R,S} \right) =$$ $$\sum {m\left( {0,2,5,7,9,11} \right)}$$ $$+ \,\,d\left( {3,8,10,12,14} \right)$$

Here, $$m$$ denotes a minterm and $$d$$ denotes a don’t care term. The number of essential prime implicants of the function $$F$$ is ______.

2
GATE CSE 2012
+2
-0.6
What is the minimal form of the Karnaugh map shown below? Assume that $$X$$ denotes a don’t care term. A
$$\overline {bd}$$
B
$$\overline {bd} + \overline {bc}$$
C
$$\overline {bd} + a\overline {bc} d$$
D
$$\overline {bd} + \overline {bc} + \overline {cd}$$
3
GATE CSE 2004
+2
-0.6
Consider a multiplexer with $$X$$ and $$Y$$ as data inputs and $$Z$$ as control input. If $$z=0$$ select input $$x,$$ and $$z=1$$ selects input $$Y$$. what are the connections required to realize the $$2-$$variable Boolean function $$f=T+R$$ without using any additional Hardware?
A
$$R$$ to $$X,$$ $$1$$ to $$Y,$$ $$T$$ to $$Z$$
B
$$T$$ to $$X,$$ $$R$$ to $$Y,$$ $$T$$ to $$Z$$
C
$$T$$ to $$X,$$ $$R$$ to $$X,$$ $$O$$ to $$Z$$
D
$$R$$ to $$X,$$ $$O$$ to $$Y,$$ $$T$$ to $$Z$$
4
GATE CSE 2003
+2
-0.6
The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of $$(xy + xz)$$ is $$4.$$ What are the minimum possible literal counts of the product -of -sum and sum -of-product representations respectively of the function given by the following Karnaugh map? Here, $$X$$ denotes “don’t care” A
$$(11, 9)$$
B
$$(9,13)$$
C
$$(9,10)$$
D
$$(11, 11)$$
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
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