1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider two cache organization: The first one is $$32$$ $$KB$$ $$2$$-way set associate with $$32$$-byte block size. The second one is of the same size but direct mapped. The size of an address is $$32$$ bits in both cases. $$A$$ $$2$$-to-$$1$$ multiplexer has latency. of $$0.6$$ $$ns$$ while a $$k$$-bit comparator has a latency of $$k/10$$ $$ns.$$ The bit latency of the set associative organization is $${h_1}$$ while that of the direct mapped one is $${h_2}.$$

The value of $${h_2}$$ is

A
$$2.4$$ $$ns$$
B
$$2.3$$ $$ns$$
C
$$1.8$$ $$ns$$
D
$$1.7$$ $$ns$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Given two three bit number $${a_2}{a_1}{a_0}$$ and $${b_2}{b_1}{b_0}$$ and $$c,$$ the carry in the function that represents the carry generate function when these two numbers are added is
A
$$\eqalign{ & {a_2}{b_2} + {a_2}{a_1}{b_1} + {a_2}{a_1}{a_0}{b_0} + {a_2}{a_0}{b_1}{b_2}{b_1} \cr & + {a_1}{a_0}{b_2}{b_0} + {a_0}{b_2}{b_1}{b_0} \cr} $$
B
$$\eqalign{ & {a_2}{b_2} + {a_2}{b_1}{b_0} + {a_2}{a_1}{b_1}{b_0} + {a_1}{a_0}{b_2}{b_1} + {a_1}{a_0}{b_2} \cr & + {a_1}{a_0}{b_2}{b_0} + {a_2}{b_0}{b_1}{b_0} \cr} $$
C
$${a_2} + {b_2} + \left( {{a_2} \oplus {b_2}} \right)\left( {{a_1} + {b_1} + \left( {{a_1} \oplus {b_1}} \right)\left( {{a_0} + {b_0}} \right)} \right)$$
D
$$\eqalign{ & {a_2}{b_2} + \overline {{a_2}} {a_1}{b_1} + \overline {{a_2}{a_1}} {a_0}{b_0} + \cr & {a_2}{a_0}\overline {{b_1}} {b_0} + {a_1}\overline {{b_2}} {b_1} + \overline {{a_1}} {a_0}\overline {{b_2}} {b_0} + {a_0}\overline {{b_2}{b_1}} {b_0} \cr} $$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let T be a depth first search tree in an undirected graph G. Vertices u and v are leaves of this tree T. The degrees of both u and v in G are at least 2. which one of the following statements is true?
A
There must exist a vertex w adjacent to both u and v in G
B
There must exist a vertex w whose removal disconnects u and v in G
C
There must exist a cycle in G containing u and v
D
There must exist a cycle in G containing u and all its neighbours in G.
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array is 0. The index of the parent of element X[i],i≠0 is?
A
⌊ i/2 ⌋
B
⌈ (i-1)/2 ⌉
C
⌈ i/2 ⌉
D
⌈ i/2 - 1 ⌉