ENGG1015: Homework 3 Dr. Kenneth Wong / Dr. Hayden So Due: 5pm, Nov 24, 2010 Turn in your homework at boxes outside Rm712, CYC Building Question 1 Digital Logic 1 Simplify the following Boolean expressions using Boolean theorems. Verify your answer by deducing the Truth Table of the expressions before and after simplifications. You should express your answers in canonical sum-of-product form. (i) AB + A B (ii) A + B(A + B) (iii) (BC + AD)(AB + CD) (iv) A + B + CD + A + B + B + C D + AB + CD Question 2 Digital Logic 2 Simplify the following Boolean expressions using Karnaugh map. Show the K-map and how the cells are circled. Express your answer in canonical sum-of-product form. (i) AB + AB (ii) (A + B)(A + B) (iii) B + BC + ABC + AB + BC + AC (iv) (ABC + ABC + AB)(A B C + ABC)(A B C + ABC) [Hint: you do not need to expand the expression to use a K-map.] Question 3 Digital System Design This question is based on Exercise 2.24 from the textbook Digital design and computer architecture. A circuit has four inputs and two outputs. The inputs, A 3:0, represent a number from 0 to 15. Output P should be TRUE if the number is prime (0 and 1 are not prime, but 2, 3, 5, and so on, are prime). Output D should be TRUE if the number is divisible by 3. In other word, the number eleven is represented when A 3 = 1, A 2 = 0, A 1 = 1, A 0 = 1 is presented in the input. Give simplified Boolean equations and Truth Table for each output. Construct a circuit that takes the 4 inputs (A 3:0 ) and produces the outputs P and D using only 2-input gates. Question 4 Digital Image Transfer Performance You have a digital photo taken from a 10 megapixel digital camera. After some inspections, you found that the picture has an aspect ratio of 16:9 and contains only 9,960,336 pixels.
ENGG1015 Homework 3 Question 5 What is the size of the digital photo in the X and Y dimension? Further investigations found that the digital photo is stored as a bitmap file on the computer using 24-bit RGB color encoding. That is, each pixel is stored using 3 bytes, each representing one of the three primrary colors. Furthermore, 128 bytes of header information was stored in the beginning of the file to store meta information such as the colorspace of the image. Given the above information and the information from Part (a), what is the size of the digital photo in terms of number of bytes? You are now sending this picture to your friend over a network. The network has a guranteed throughput of 10 Mbytes/s, and a latency of 10 ms. How long does it take for the first byte to arrive at your friend? How long does it take for the entire file to be transferred over the network? Question 5 Network Performance Two computers, Computer A and Computer B, are connected through a direct network. This network has a maximum bandwidth of 10 Mbps, a fixed packet size of p bytes, and a fixed header size of h bytes. Assume that Computer A and Computer B are physically separated by 1200 km, about the distance from Hong Kong to Shanghai. Using the fact that the speed of light is roughly 3 10 8 m/s, how long does it take the first bit of information from Computer A to arrive at Computer B? How long does it take one packet sent by Computer A to arrive completely at Computer B? Will your answer in be changed if Computer A is sending just 1 byte to Computer B? Part(d) What is the latency of the network. Part(e) In a packet switched network, bandwidth must be used up to transmit headers as well as the data payloads. The effective amount of data that can be sent through a network is therefore smaller than its stated bandwidth, and is called its througput. Given this definition, what is the theoretical maximum throughput that this network can transmit data at? Part(f) Your project partner wrote a piece of code that transmits a large file of (10000 p) bytes from Computer A to Computer B. As someone who dares not to make large moves, your project partner wrote the code such that each packet transmits exactly 1 byte of the file. Assuming packets can be transmitted on the network one right after each other, what is the throughput of transmitting the large file. EEE/ENGG1015/2010 Page 2 of 5
ENGG1015 Homework 3 Question 6 Part(g) Being someone who always like things big, you rewrote the code such that each packet transmits exactly p bytes. What is the throughput of transmitting the large file in this case? Part(h) There are two main applications planned to run between Computer A and B: (i) a multi-user online game, and (ii) large file transfers. Based on the results from the previous sections, explain how the following factors will affect the performance and user experience in the above two scenarios: p, h, the bandwidth of the network, and the speed of light. Question 6 1. Which of the following statement(s) about circuit switching is (are) correct? (i) Resources allocated for the connection must be shared among users. (ii) Performance is guaranteed for the data using the link. (iii) Connection setup is required before data transmission. B. (ii) and (iii) C. (i) and (iii) 2. Which of the following protocol layer is not needed in a router? A. Physical layer B. Link layer C. Network layer D. Transport layer 3. Which of the following statement(s) about mobile phone base station is(are) true? (i) When a mobile phone is turned on, it must associate itself with a base station. (ii) In a GSM system, adjacent cells usually communicate to mobile phones at different frequency channel. (iii) Base stations are connected to each other with special wireless channels. B. (i) and (ii) only C. (ii) and (iii) only 4. Which of the following layer is not part of the OSI network layer? A. Transport layer B. Presentation layer C. Web layer D. Link layer 5. Which of the following is a not a task of the TCP protocol? A. Provides reliable transmission B. Hides the details of the underlying network protocol from the upper layer. C. Provides state information about a connection D. Decrypt a packet 6. Which of the following information can be extracted from a TCP packet? (i) Ethernet address of the source computer (ii) Destination IP address (iii) HTTP command EEE/ENGG1015/2010 Page 3 of 5
ENGG1015 Homework 3 Question 7 A. (i) B. (iii) C. (i) and (ii) 7. Concerning the common wireless LAN 802.11 standards, which of the following statement(s) is(are) true? (i) It can be considered as an application layer protocol. (ii) It uses a shared medium for physical connection (iii) It exhibits Hidden node and Exposed node problems that are not presented in wired network. B. (ii) only C. (ii) and (iii) 8. Based on the end-to-end argument, which entity in the network connection should be responsible to guarantee reliable communication between two end hosts? A. The end hosts B. The ISP that connects the end hosts to the Internet C. The routers between the hosts D. The end user 9. Which of the following are responsibilities of a network layer? (i) Provides services to the layer above. (ii) Provides services to the layer below. (iii) Utilizes services from the layer above. (iv) Utilizes services from the layer below. A. (i), (iii) B. (i), (iv) C. (ii), (iii) D. (ii), (iv) 10. When two end hosts A and B communicate with each other, the module in layer n in A always communicate with: A. the layers below n in B B. the layers above n in B C. the layer n in B D. any layer in B as long as the users request it. Question 7 Remember: this is an individual homework. You should be answering this question by yourself. What is your project group name? What is your project group number? In less than 200 words, describe how the Rube Goldberg machine you and your partners has built for the course works? Starting from the push button, how does it lead to the final popping of the balloon? In less than 300 words, describe your role in the project. What have you built? Which part of the design was your idea? Also, briefly explain how your group has divided the workload among the group members. EEE/ENGG1015/2010 Page 4 of 5
ENGG1015 Homework 3 Question 7 Part(d) Extra Credits Your answer to this question is not mandatory, but your comments will help us shape the future of this course and earn you some extra credits. (i) How do you like the project? (ii) Do you think it has helped you in understanding how basic electronic circuit works? (iii) Did you have fun in the project? (iv) Any suggestion on how the project can be improved in the future? EEE/ENGG1015/2010 Page 5 of 5