GATE CSE topic:computing PYQs & Answers — Page 65

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Questions 641–650 of 975. Imported answers require independent review unless marked reviewed.

Topic practice 975 questionsPage 65 of 98

In a pushdown automaton

, a transition of the form

Diagram for Computer Science and Information Technology question 51

where

, and

, represents

Consider the following pushdown automaton over the input alphabet

and stack alphabet

Diagram for Computer Science and Information Technology question 51 (figure 2)

The number of strings of length 100 accepted by the above pushdown automaton is __________.

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Consider the following augmented grammar with

as the set of terminals.

Let

. The number of items in the set

is ____________.

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Consider the following matrix.

The largest eigenvalue of the above matrix is __________.

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Consider a Boolean function

such that

The number of literals in the minimal sum-of-products expression of

is ____________.

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A five-stage pipeline has stage delays of 150, 120, 150, 160 and 140 nanoseconds. The registers that are used between the pipeline stages have a delay of 5 nanoseconds each. The total time to execute 100 independent instructions on this pipeline, assuming there are no pipeline stalls, is __________ nanoseconds.

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Consider a pipelined processor with 5 stages, Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Write Back (WB). Each stage of the pipeline, except the EX stage, takes one cycle. Assume that the ID stage merely decodes the instruction and the register read is performed in the EX stage. The EX stage takes one cycle for ADD instruction and two cycles for MUL instruction. Ignore pipeline register latencies.

Consider the following sequence of 8 instructions:

ADD, MUL, ADD, MUL, ADD, MUL, ADD, MUL

Assume that every MUL instruction is data-dependent on the ADD instruction just before it and every ADD instruction (except the first ADD) is data-dependent on the MUL instruction just before it. The speedup is defined as follows:

The speedup achieved in executing the given instruction sequence on the pipelined processor (rounded to 2 decimal places) is ____________.

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A sender (

) transmits a signal, which can be one of the two kinds:

and

with probabilities 0.1 and 0.9 respectively, to a receiver (

). In the graph below, the weight of edge

is the probability of receiving

when

is transmitted, where

. For example, the probability that the received signal is

given the transmitted signal was

, is 0.7.

Diagram for Computer Science and Information Technology question 54

If the received signal is

, the probability that the transmitted signal was

(rounded to 2 decimal places) is __________.

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Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (=

bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modeled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ____________.

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Consider the following instruction sequence where registers R1, R2 and R3 are general purpose and MEMORY[X] denotes the content at the memory location X.

Instruction	Semantics	Instruction Size (bytes)
MOV R1, (500)	R1 ← MEMORY[500]	4
MOV R2, (R3)	R2 ← MEMORY[R3]	4
ADD R2, R1	R2 ← R1+R2	2
MOV (R3), R2	MEMORY[R3] ← R2	4
INC R3	R3 ← R3+1	2
DEC R1	R1 ← R1-1	2
BNZ 104	Branch if not zero to the given absolute address	2
HALT	Stop	1

Assume that the content of the memory location 500 is 10, and the content of the register R3 is 300. The content of each of the memory locations from 300 to 3010 is 50. The instruction sequence starts from the memory location 100. All the numbers are in decimal format. Assume that the memory is byte addressable.

After the execution of the program, the content of memory location 3010 is __________.

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In a directed acyclic graph with a source vertex

, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex

other than

, the quality-score of

is defined to be the maximum among the quality-scores of all the paths from

. The quality-score of

is assumed to be 1.

Diagram for Computer Science and Information Technology question 55

The sum of the quality-scores of all the vertices in the graph shown above is ____________.

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GATE CSE topic:computing PYQs

Question 51

Question 51

Question 52

Question 52

Question 53

Question 53

Question 54

Question 54

Question 55

Question 55