Honors Seminar (Humanities 320; Spring, 2005) The Digital Revolution
Review Examination I
Department of Mathematics and Computing
York College (CUNY)
Jamaica, New York 11451
web page: www.york.cuny.edu/~malk
1. Be prepared to give a brief discussion of the ways that the following technologies have changed human society:
(Give the approximate date when the technology was first discovered, and when it took root)
b. Electric distribution network
j. Space rockets
k. Earth orbiting satellites
l. Cell phone
m. ATM machine
q. Fax machines
r. Moveable type
i. Do you think each of these technologies represented progress for mankind? Explain your position.
ii. Some of the technologies above fully digital, some are hybrid analog and digital, and some are analog. What are some of the pros and cons of digital technologies?
2. Discuss briefly the difference between the number concept and ways of representing numbers
3. Do the following number conversions:
a. (1110111)2 = (?)10
b. (1101)5 = (?)10
c. (101)10 = (?)2
d. (123)4 = (?)10
e. (113)10 = (?)5
4. Verify whether or not the following UPC codes are "legal" and when the check digit is not proper, what one should be there:
a. 7-18103-02922-3 (Staples 3-tab file folders)
b. 0-74319-11665-3 (Staples 1/3 cut file folders)
c. 0-78973-21157-6 (Staples multicolored file folders)
5. Use the zip code dictionary to convert the following to barcodes. (Be sure to include the check digit and the guard bars.)
d. Why did the original zip code of 5 digits have to be expanded?
e. In a 5 digit zip code what roles do the first three digits have? What role do the last 2 digits have?
f. Be prepared, using the zip code dictionary, to decode a barcoded zip code.
g. Explain which of the check digit systems used for UPC, zip code, and ISBN is the "strongest," ..., "weakest."
h. What is the difference between an error detection system and an error correction system?
6. Find the check digits for the following ISBN numbers.
a. 0-7897-1562 - ?
b. 0-8218-2904 - ?
c. 0-375-40404 - ?
7. Convert the three ISBN numbers above to EAN -13 universal product codes and determine the check digit for each.
Answers for the check digits:
8. a. Design a fixed length binary code to send the decimal stream of digits below, and encode the stream:
b. Construct a Huffman binary code for compressing the string above. How many bits are saved over what you need to send the message via your system in a.
c. Repeat a. and b. above for the sequence of DNA letters below:
9. Do the computations:
a. 37 ? mod 8
b. 337 ? mod 11
c. 237 ? mod 5
d. -37 ? mod 8
e. -237 ? mod 5
f. -67 ? mod 14
g. Find the positive remainder when:
i. 18 is divided by 7
ii. -17 is divided by 4
iii. -1221 is divided by 19
9. Give some examples of situations where barcodes are being used and explain why using barcodes off advantages over what was done before the introduction of barcodes.
10. Why has capitalism evolved the use of standards? Give some examples of situations where standards are being used?
11. Given examples of situations where error correction technology is used.
12. Give some examples of situations where data compression technology is used.
13. Encode the image below from top to bottom and left to right using the code shown:
a. Use as short a binary code as possible to encode this picture scanning from top to bottom and left to right.
b. What data stream would be sent if you decided to error protect this image with the code:
a = 01010
"blank" = 00001
c. Compute the Hamming distance between each of these code words. Will this code be able to correct and/or detect errors? If so, how many errors can it correct?
d. Compute the "sphere" of radius one about each of these code words, and list the code words in each of these spheres. Show that this is not a perfect code by writing down the 8 code words that are not part of any sphere of radius 1 about a code word. Which if any of these strings are equidistant from two or more code words?
e. If one wanted to compress this picture before using an error correction system on it, what huffman code one one use? How many bits would this save? What would be done if you wanted to be able to correct one error after compression. How would you carry this out?
f. Using the code for a, b, c, and "blank" above, and assuming the following bit steam arrives, reconstruct the picture that was sent:
14. Compute the Hamming distance between each pair of the strings below:
a. 11000011 and 10101100
b. 11001110 and 11101100
c. ACGTTAG ACTGATG
d. TAGTAGGAT AATTTATAT
e. 1122336644552 2121122334553
f. ++++***++ ++****++*+
15. Explain why the Hamming distance is inadequate to be used in work regarding genes in the attempt to construct the genome of different species.
16. What is meant by the phrase "genetic code?" In the genetic code is there exactly one code word for each amino acid? What other role(s) do the code words play?
17. Is Morse code a variable or fixed length code?
18. What is the difference between a code a cipher?