1
GATE CSE 2016 Set 1
+1
-0.3
Consider the Boolean operator $$\ne$$ with the following properties:
$$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \ne x = 0$$ and $$x \ne \overline x = 1.$$ Then $$x \ne y$$ is equivalent to
A
$$x\overline y + \overline x y$$
B
$$x\overline y + \overline x \overline y$$
C
$$\overline x y + xy$$
D
$$xy + \overline x \overline y$$
2
GATE CSE 2015 Set 3
+1
-0.3
Let $$\ne$$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$𝑋$$ and $$𝑌$$ are Boolean variables. Consider the following two statements. \eqalign{ & \left( {S1} \right)\,\,\,\,\,\,\,\left( {P \ne Q} \right) \ne R = P \ne \left( {Q \ne R} \right) \cr & \left( {S2} \right)\,\,\,\,\,\,\,Q \ne R = R \ne Q \cr}\$

Which of the following is/are true for the Boolean variables $$𝑃, 𝑄$$ and $$𝑅$$?

A
Only $$S1$$ is true
B
Only $$S2$$ is true
C
Both $$S1$$ and $$S2$$ are true
D
Neither $$S1$$ nor $$S2$$ are true
3
GATE CSE 2014 Set 1
+1
-0.3
Consider the following Boolean expression for $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overline P Q\overline R S.$$
The minimal sum-of-products form of $$F$$ is
A
$${PQ} + QR + QS$$
B
$$P + Q + R + S$$
C
$$\overline P + \overline Q + \overline R + \overline S$$
D
$$\overline P R + \overline P \overline R S + P$$
4
GATE CSE 2014 Set 3
+1
-0.3
Consider the following combinational function block involving four Boolean variables $$x, y, a,$$
$$b$$ where $$x, a, b$$ are inputs and $$y$$ is the output.
Which one of the following digital logic blocks is the most suitable for implementing this function?
A
B
Priority encoder
C
Multiplexer
D
Flip-flop
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