1
GATE CSE 2014 Set 3
+2
-0.6
Consider the transactions T1, T2, and T3 and the schedules S1 and S2 given below.

T1 : r1 (X) ; r1 (Z) ; w1 (X) ; w1 (Z)

T2 : r2 (X) ; r2 (Z) ; w2 (Z)

T3 : r3 (X) ; r3 (X) ; w3 (Y)

S1: r1(X); r3(Y); r3(X); r2(Y); r2(Z); w3(Y); w2(Z); r1(Z); w1(X); w1(Z)

S2: r1(X); r3(Y); r2(Y); r3(X); r1(Z); r2(Z); w3(Y); w1(X); w2(Z); w1(Z)

Which one of the following statements about the schedules is TRUE?
A
Only S1 is conflict-serializable.
B
Only S2 is conflict-serializable.
C
Both S1 and S2 are conflict-serializable.
D
Neither S1 nor S2 is conflict-serializable.
2
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
3
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
$$\overline {P \oplus Q}$$
4
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
$$\overline P \overline Q \overline S + \overline P QS + PQS + P\overline Q \overline S$$
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