1
GATE CSE 2016 Set 1
+2
-0.6
Consider the two cascaded $$2$$-to-$$1$$ multiplexers as shown in the figure.

The minimal sum of products form of the output $$X$$ is

A
$$\overline P \overline Q + PQR$$
B
$$\overline P Q + QR$$
C
$$PQ + \overline P \overline Q R$$
D
$$\overline Q \overline R + PQR$$
2
GATE CSE 2014 Set 1
+2
-0.6
Consider the $$4$$-to-$$1$$ multiplexer with two select lines $${S_1}$$ and $${S_0}$$ given below

The minimal sum-of-products form of the Boolean expression for the output $$F$$ of the multiplexer is

A
$$\overline P Q + Q\overline R + P\overline Q R$$
B
$$\overline P Q + \overline P Q\overline R + PQ\overline R + P\overline Q R$$
C
$$\overline P QR + \overline P Q\overline R + Q\overline R + P\overline Q R$$
D
$$PQ\overline R$$
3
GATE CSE 2007
+2
-0.6
Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $$n$$ variables. What is the minimum size of the multiplexer needed?
A
$${2^n}$$ line to $$1$$ line
B
$${2^{n + 1}}$$ line to $$1$$ line
C
$${2^{n - 1}}$$ line to $$1$$ line
D
$${2^{n - 2}}$$ line to $$1$$ line
4
GATE CSE 2006
+2
-0.6
Consider the circuit above. Which one of the following options correctly represents $$f(x,y,z)?$$
A
$$x\overline z + xy + \overline y z$$
B
$$x\overline z + xy + \overline {yz}$$
C
$$xz + xy + \overline {yz}$$
D
$$xz + x\overline y + \overline y z$$
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