1
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
2
GATE CSE 2014 Set 3
+2
-0.6
Let $$\oplus$$ denote the exclusive $$OR\left( {XOR} \right)$$ operation. Let $$'1'$$ and $$'0'$$ denote the binary constants. Consider the following Boolean expression for $$F$$ over two variables $$P$$ and $$Q$$:
$$F\left( {P,Q} \right) = \left( {1 \oplus P} \right) \oplus \left( {P \oplus Q} \right) \oplus \left( {P \oplus Q} \right) \oplus \left( {Q \oplus 0} \right)$$

The equivalent expression for $$F$$ is

A
$$P+Q$$
B
$$\overline {P + Q}$$
C
$${P \oplus Q}$$
D
$$\overline {P \oplus Q}$$
3
GATE CSE 2014 Set 3
+1
-0.3
Consider the following interm expression of $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15}$$
The minterms $$2, 7, 8$$ and $$13$$ are 'do not care' terms. The minimal sum-of-products form for $$F$$ is _______
A
$$Q\overline S + \overline Q S$$
B
$$\overline Q \overline S + QS$$
C
$$\overline Q \overline R \overline S + \overline Q R\overline S + Q\overline R S + QRS$$
D
$$\overline P \overline Q \overline S + \overline P QS + PQS + P\overline Q \overline S$$
4
GATE CSE 2014 Set 3
+2
-0.6

The above synchronous sequential circuit built using $$JK$$ flip-flops is initialized with $${Q_2}{Q_1}{Q_0} = 000.\,\,$$ The state sequence for this circuit for the next $$3$$ clock cycles is

A
$$001,010,011$$
B
$$111,110,101$$
C
$$100,110,111$$
D
$$100,011,001$$
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