GATE CSE 2014 Set 3 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-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. GATE CSE 2014 Set 3 Digital Logic - Boolean Algebra Question 46 English

GATE CSE 2014 Set 3 Digital Logic - Boolean Algebra Question 46 English

Which one of the following digital logic blocks is the most suitable for implementing this function?

Full adder

Priority encoder

Multiplexer

Flip-flop

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-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

$$P+Q$$

$$\overline {P + Q} $$

$${P \oplus Q}$$

$$\overline {P \oplus Q} $$

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

GATE CSE 2014 Set 3 Digital Logic - Sequential Circuits Question 20 English

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

$$001,010,011$$

$$111,110,101$$

$$100,110,111$$

$$100,011,001$$

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

Let $$X$$ and $$Y$$ be finite sets and $$f:X \to Y$$ be a function. Which one of the following statements is TRUE?

For any subsets $$A$$ and $$B$$ of $$X$$, $$\left| {f\left( {A \cup B} \right)} \right| = \left| {f\left( A \right)} \right| + \left| {f\left( B \right)} \right|$$

For any subsets $$A$$ and $$B$$ of $$X$$, $${f\left( {A \cap B} \right)}$$ $$=$$ $$f\left( A \right) \cap f\left( B \right)$$

For any subsets $$\left| {f\left( {A \cap B} \right)} \right| = \min \left\{ {\left| {f\left( A \right)} \right|,\left| {f\left( B \right)} \right|} \right\}$$

for any subsets $$S$$ and $$T$$ of $$Y$$, $${f^{ - 1}}\left( {S \cap T} \right) = {f^{ - 1}}\left( S \right) \cap {f^{ - 1}}\left( T \right)$$

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