1
GATE CSE 2004
MCQ (Single Correct Answer)
+1
-0.3
The Boolean function $$x'y' +xy +x'y$$ is equivalent to
A
$$x'+y'$$
B
$$x+y$$
C
$$x+y'$$
D
$$x'+y$$
2
GATE CSE 2004
MCQ (Single Correct Answer)
+2
-0.6
Which are the essential prime implicants of the following Boolean function? $$F\left( {a,b,c} \right) = {a^1}c + a{c^1} + {b^1}c$$
A
$$a'c$$ and $$ac'$$
B
$$a'c$$ and $$b'c$$
C
$$a'c$$ only
D
$$ac'$$ and $$bc'$$
3
GATE CSE 2004
MCQ (Single Correct Answer)
+5
-1.5
A circuit outputs a digit in the form of $$4$$ bits. $$0$$ is represented by $$0000$$, $$1$$ by $$0001..., $$ $$9$$ by $$1001.$$ A combinational circuit is to be designed which takes these $$4$$ bits as input and outputs $$1$$ if the digit $$ \ge 5,$$ and $$0$$ otherwise. If only $$AND,$$ $$OR$$ and $$NOT$$ gates may be used, what is the minimum number of gates required?
A
$$2$$
B
$$3$$
C
$$4$$
D
$$5$$
4
GATE CSE 2004
MCQ (Single Correct Answer)
+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 $$Z$$
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