Download Electronic Engineering Exam - Computer Engineering Section for BEng (Hons) and more Exams Computer Science in PDF only on Docsity!
Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering – Award
(NQF – Level 8)
Autumn 2007
Computer Engineering
(Time: 3 Hours)
Read instructions carefully Section A : Answer any TWO questions Section B: Answer any TWO questions Use separate answer books for Sections A and B All questions carry equal marks
Examiners: Prof. G. Hurley Dr. S. Foley Dr. D. Pesch Mr. F. O’Reilly
Section A
Answer two (2) questions from this section.
Q1. (a) You have been assigned the task of evaluating an interconnection network, which might extend from 100 to 1000 processing nodes. Calculate the complexity (total number of switches) of both a Cross-bar and Omega network for this task. [6 marks] (b) Vector processors provide for high performance vector operations. What are the advantages of vector processors and explain why these are suitable for execution in array architectures. [6 marks] (c) You have been asked to devise an algorithm to compute the following calculation across a floating point vector A with 500,000 elements. You have available a Private Memory system with 250 processor nodes. 500 , (^0002)
x 1
y = (A[x])^2 (A[ 500 , 000 −x])
= Develop an algorithm using pseudo code or pseudo C code which could execute on one of these processor nodes. Describe the partitioning of the problem, the data distribution over the system and provide the code to achieve the communication between the nodes to calculate the final result. [13 marks] [Total: 25 marks]
Q2. (a) Explain using diagrams, the UMA and NUMA architectures, justify which architecture is more common and give the term commonly used to describe it. [6 marks]
(b) In a paged memory management system, explain briefly the design process in deciding the size of pages, the numbers of pages, the number of page frames and page faults/replacements. [8marks] A paging based virtual memory system has the following utilisations. CPU Utilisation 20% Paging Disk 85% Other I/O 5%
Explain what is happening and what causes it. What steps if any do you think could be taken to improve CPU utilisation? [4 marks]
(c) For Massive Parallel Systems, scalability is of major importance. Using work and efficiency curves describe your understanding of it and how it relates to efficiency for Constant, Sub- Linear, Linear and Exponential work-loads. What are the boundaries on scalability and how do these affect algorithm design. [7 marks] [Total: 25 marks]
Q3. (a) A 800MHz CPU core, has a 5 stage instruction fetch/decode queue. Branches in code occurs with a 20 % frequency and impose a 4 cycle bubble. All other instructions execute with a CPI of 1. To improve performance a branch prediction unit is proposed. This will require reducing the clock rate to 600 MHz but will be able to predict 90% of branches with no-penalty, mis-prediction will impose a 7 cycle flush/re-load penalty. Calculate whether it is worthwhile adding the branch-prediction unit. [8 marks]
Section B
Q4. (a) Briefly explain the purpose of line codes in data communication links and state two performance measures. Develop a state transition diagram (finite state machine) representation of bipolar AMI coding. [8 marks]
(b) A CRC is constructed to generate a 5-bit FCS for an 11-bit message. The generator polynomial is G(X) = X^5 +1. (i) Draw the shift register circuit that implements the CRC. (ii) Generate the FCS for the data bit sequence 11111111111 (left most bit is the least significant) using the generator polynomial. (iii) Now assume that bit 5 (counting from the LSB) in the bit sequence is in error and show that the detection algorithm detects the error. [8 marks] (c) Consider a direct computer communication link between two distant sites of a company. A go-back-N ARQ technique with a window length N = 15 is used to provide a reliable communication link. The data rate is 512kbit/s, frames are 1024bits including overheads, the speed of the signal is 2⋅ 10 8 m/s, and the distance between the two sites is 3000km. Calculate the maximum Bit Error Probability (not frame error probability) that can persist on this link in order to guarantee a minimum throughput of U = 0.8. NOTE: In your calculation assume that acknowledgement frames are never in error and that their transmission delay can be neglected. [9 marks]
Q5. (a) Consider a LAN with a large number of PCs and a single database server. The server receives 100 requests per minute during normal operation according to a Poisson process. The server requires 0.4 seconds on average to process a request. The processing time is exponentially distributed. (i) Calculate the total time each user has to wait until she receives a reply to her query using a suitable queuing model. (ii) By what factor can the request rate be increased if during peak times users are willing to wait twice as long for a reply compared to the normal case of part i) of the question? Assume that communication delay on the LAN is negligible. [10 marks] (b) The input to a router in a computer network is an aggregate data packet stream that can be modelled by a Poisson process with arrival rate λ= 24 packets/sec. The length of the data packets is exponentially distributed with mean L = 512bytes. (i) Assume that the router has m = 4 output lines of data rate R = 32kbit/s each. Calculate the probability that arriving packets have to queue before transmission. (ii) Assume that the four output lines are now combined into a single output line of data rate R = 128kb/s. Also for this case calculate the probability that an arriving packet has to queue. [15 marks]
Q6. (a) A transmission system, comprising of a single transmission line and a multiplexer, is shared among 10 computer systems. Data packets of size 128bytes are generated by each computer systems according to a Poisson process with rate λ = 1.25/sec. The multiplexer aggregates the packet streams coming from the computer systems and transmits data at 6 different data rates; rate R 1 = 4.8kbit/s is available 15% of the time, rate R 2 = 9.6kbit/s, 25% of the time, rate R 3 = 19.2kbit/s, 20% of the time, rate R 4 = 28.8kbit/s, 20% of the time, rate R 4 = 56kbit/s, 15% of the time, and rate R 5 = 64kbit/s is available 5% of the time.
NOTE: Some formulae you might find useful in answering questions 4, 5, and 6.
frametransmission time a =signalpropagationdelay Stop-and-wait ARQ Go-back-N ARQ Selective-repeat ARQ
N > 2 a + 1 a U P 1 2
1
= − aP U P 1 2
1
= − U^ =^1 − P
N < 2 a + 1 a U P 1 2
1
= − (^ ) ( a )( P NP ) U N P
1 ( ) 2 1
1
= − a U N P
Little’s theorem: A = λ T and AQ = λ W
M/M/1/∞ Queuing System: state probability of Markov chain pi = ( 1 −ρ) ρ i
A = 1 − , μ
M/M/m/∞ Queuing system: AQ = P Q 1 −ρ ρ and A = m ρ + P Q 1 −ρ ρ
Probability of queuing in M/M/m: P = p (^0) m (! m^ ( 1 ρ−)ρ)
m Q , where^
( ) ( ) ( )
−
1 (^0 0)!! 1
m i
i m m
m i p m
ρ ρ and
= m
Pollazcek-Khinchin formula: W = (^2) ( 1 λ − X λ X )
2 and T = X + W
with ∑ ( )
∞
k 0 k^ k
X X PX and ( (^) k ) k k^
X ∑ X PX
∞
0
2
The solutions of the quadratic equation ax^2 + bx + c = 0 are x b 2 ba^4 ac
2 1 , 2 =− ±^ −
