1
GATE CSE 2015 Set 2
Numerical
+2
-0
A half adder is implemented with $$XOR$$ and $$AND$$ gates. A full adder is implemented with two half adders and one $$OR$$ gate. The propagation delay of an $$XOR$$ gate is twice that of an $$AND/OR$$ gate. The propagation delay of an $$AND/OR$$ gate is $$1.2$$ microseconds. A $$4$$-bit ripple-carry binary adder is implemented by using four full adders. The total propagation time of this $$4$$-bit binary adder in microseconds is____________ .
2
GATE CSE 2015 Set 1
+2
-0.6

The binary operator $$\ne$$ is defined by the following truth table.

p q p$$\ne$$q
0 0 0
0 1 1
1 0 1
1 1 0

Which one of the following is true about the binary operator $$\ne$$?

A
Both commutative and associative
B
Commutative but not associative
C
Not commutative but associative
D
Neither commutative nor associative
3
GATE CSE 2015 Set 1
+2
-0.6

Consider the operations

$$f\left( {x,y,z} \right) = X'YZ + XY' + Y'Z'$$ and
$$g\left( {x,y,z} \right) = X'YZ + X'YZ' + XY$$.

Which one of the following is correct?

A
Both $$\left\{ f \right\}$$ and $$\left\{ g \right\}$$ are functionally complete
B
Only $$\left\{ f \right\}$$ is functionally complete
C
Only $$\left\{ g \right\}$$ is functionally complete
D
Neither $$\left\{ f \right\}$$ nor $$\left\{ g \right\}$$ is functionally complete
4
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
$$\overline {P \oplus Q}$$
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