1
GATE CSE 2016 Set 1
+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
$$\Theta \left( n \right)$$
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 2015 Set 2
Numerical
+2
-0
The number of min-terms after minimizing the following Boolean expression is _______________ . $$\left[ {D' + AB' + A'C + AC'D + A'C'D} \right]'$$\$