Welcome to the MODD Zone

(Mathematics Of Digital Data, Period D)
Web address shortcut for this page: www.modd.net/56modd

Are you nervous when you see NCWEE? concerned when you see CIRC? perturbed when you see PBC? Visit Mr. Hansen’s fabled abbreviations page to make sense of those cryptic markings you see on your papers.


Schedule at a Glance (see archives for older entries)
Written assignments should follow the HW guidelines.


F 1/6/06

HW due (for your own benefit): Please study your old tests. In case you have lost track of your copies, blank versions of most of the problems are available here.

Unit 0x00: Logical Building Blocks (9/20/05)
Unit 0x10: Bits, Bytes, Hex, and Hertz (9/29/05)
Unit 0x20: What’s So Great About Digital? (10/6/05)
Unit 0x30: Audio (10/20/05)
Unit 0x40: Compression (10/31/05)
Unit 0x50: Video (11/11/05)
Unit 0x60:Computation (12/1/05)
Units 0x70, 0x80, 0x90: Cryptography, Error Correcting Codes, Information Theory (12/14/05)
Alternate Version of Multi-Unit Test for 0x70, 0x80, 0x90 (12/16/05)


T 1/10/06

Midterm Exam, 11:00 a.m., Room S. The exam will last approximately 1 hour. If you need more time, I will allow you to use the full 2-hour time allotted.

The exam is cumulative. You may use your calculator, and the memory will not be cleared. Therefore, if you wish to make notes in your calculator’s memory, you may. However, I caution you that relatively few of the questions will be of the simple “recall” type. I am more likely to ask questions that require thought and may involve linking topics from multiple units. Here are some sample questions:

1. Explain the relationship between bit depth and the size of the color palette that is possible. Give several examples.

2. Explain, in general terms, what RGB and YCbCr are (i.e., the vocabulary word) and why both systems are in common usage.

3. What vocabulary word refers to the effective information density of a data file (i.e., information content in each byte, in each 64-bit block, or in some other suitable common measure)? Can the size of a ZIP file be used as a rough indicator of this density? If not, how would you modify the ZIP file size so that it could provide a good estimate?

4. A piece of graph paper is photographed. Ideally, we would expect to see nothing but a grid of squares. However, suppose that the image shows a mixture of squares and odd-sized larger rectangles. How is this possible? What vocabulary word(s) may apply to this situation?

5. Design an RLE protocol for encoding a 12
´ 12 monochrome bitmap of your own choosing. Then encode your bitmap in hex and calculate the compression ratio that you achieved.

6. What mathematicians are remembered as (a) the author of the Incompleteness Theorem, (b) the father of information theory, and (c) the greatest computer scientist on the Enigma project? Give an additional sentence for each. For example, state the Incompleteness Theorem in your own words.

7. Shannon’s Theorem, which we unfortunately did not have time to discuss, gives a maximum data rate (in bps) as a function of the available bandwidth of a channel and the S/N ratio. Explain how this explains why your cell phone loses fewer packets when you have a fresh battery (as opposed to an almost dead battery), and why you may experience more “dead zones” during times of the day when cell phone usage is at its peak. Try to use the word “multiplexing” in your answer.

8. State Ohm’s Law and use it to calculate the maximum current (and from that, the maximum power) that a 12V battery will deliver to a 10 K
W resistive load. Is this enough to kill a person? What if your hands are very salty or wet, and you touch the terminals of a 12V car battery?

9. DES, and especially triple-DES, are considered to be good ________ protocols. We say this because a 64-bit key (actually _______ bits since every 8th bit in the key is ignored) causes a _____________ of bits that is so inscrutable that an adversary who does not have the key will have no faster way to recover the original message than to perform a “________ ________” search through about half of the ________ possible keys in the case of DES, or ________ possible keys in the case of triple-DES.

10. Explain why ISBN and VIN check digits are calculated with weightings instead of with simple parity checks.


Links Based on Class Discussions:
-- Latest revision of our MODD course outline
-- Homemade “Segway”-like balancing scooter uses a fair amount of calculus!

Serious Links:
-- Summer math camps for talented high school students
-- Click here for other serious links

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Last updated: 07 Jan 2006