1
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

A
$$\overline {P \oplus Q} = P \odot Q$$
B
$$\overline P \oplus Q = P \odot Q$$
C
$$\overline P \oplus \overline Q = P \oplus Q$$
D
$$\left( {P \oplus \overline P } \right) \oplus Q = \left( {P \odot \overline P } \right) \odot \overline Q $$
2
GATE CSE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider a carry lookahead adder for adding two $$n$$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is
A
$$\Theta \left( 1 \right)$$
B
$$\Theta \left( {\log \left( n \right)} \right)$$
C
$$\Theta \left( {\sqrt n } \right)$$
D
$$\Theta \left( n \right)$$
3
GATE CSE 2015 Set 1
MCQ (Single Correct Answer)
+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
4
GATE CSE 2015 Set 1
MCQ (Single Correct Answer)
+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
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