Due: 2006 September 8th, beginning of class!
Name: ____________________________________
Score: _____ / 75 = _____ / 100
Submit a hand-written or typed set of answers. (Staple multiple sheets together - do not submit them as loose, separate pages.) Do not simply send e-mail, unless you have a valid excuse for not coming to class.
As appropriate, show the work (the logical steps required) for answering each question. A correct answer, without showing how you got it, will receive at most 50% credit. If you show a formula, give the reason that it is the correct formula to use.
Questions: ( 5 pts each)
1. What are two different interpretations of the prefixes kilo, mega, and giga? Define a context in which each interpretation is used.
2. What is the bandwidth of telephone voice?
3. List two common image formats. If they use compression, contrast the two.
Problems:
10 pts - 1. How many bits will it take to represent the following sets of outcomes?
a. The uppercase alphabet A, B…Z
b. The digits 0, 1, …9
c. The seconds in a 24 hour day.
d. The people in the United States ( about 248,000,000)
e. Population of the world ( about 6 billion)
25 pts - 2. When examining X-rays, radiologists often deal with four to six images at a time. For a faithful digital representation of an X-Ray photograph, a pixel array of 2048 by 2048 is typically used with a gray scale of intensity for each pixel of 12 bits. As you would hope, radiologists do not look kindly on compression that degrades quality.
a. How many levels of gray scale are represented by 12 bits?
b. How many bits does it take to represent an X-Ray based on these parameters
c. Suppose five X-Rays have to be sent to another site over a T-1 line (1.544Mbps). How long would it take, at best ignoring overhead.
d. Suppose now that we wish to build a communications system that will provide the five X-Rays of part c upon demand; that is, that from the time the X-Rays are requested we want them available within 2 seconds. What is the lowest channel rate that can support this demand?
e. The next generation of displays for X-Rays is planned for 4096 by 4096 pixels with a 12 bit gray scale. What does the answer to part d become when using this resolution?
25 pts - 3. A multimedia version of a multivolume reference book is being prepared for storage on compact disk (CD). Each disk can store about 700MB ( megabytes). The input to each volume consists of 1000 pages of text typed 10 characters to the inch, 6 lines to the inch, on 8 by 11 inch paper with one inch margin on each side. Each volume also has about 100 pictures, which will be displayed in color at SXGA resolution (1280x1024 pixels, 32b/pixel) moreover, each volume is enhanced for the CD version with 30 minutes of audio of teleconferencing quality (16,000 smp/sec, 6 b/smp).
a. How many bits are there on a 700 megabyte CD (1 megabyte = 2 **20 bytes)
b. Without compression and ignoring overhead, how many volumes can be put on one CD?
c. Suppose the material is to be transmitted over a T-1 facility (1.544 Mbps). How long will it take, exclusive of overhead, to transmit a volume?
d. Suppose the text can be compressed at a 3:1 rate, the pictures at 10:1, and the audio at 2:1. How many volumes, exclusive of overhead, will fit on a CD?
e. How long will it take to transmit a compressed volume on a T-1 channel?
Note: Overhead are extra bits that are used for error detection and for providing control of information flow.We haven’t talked about that yet so don’t worry about overhead.