MODD / Mr. Hansen 10/21/2010

Name: _______________________

General Instructions: Raise your hand if you have a question. Write answers in the space provided. If you need additional room, write "OVER" and use reverse side.

Part I: Essay.

1.	Explain, in general terms, how undersampling of a digital image can lead to “banding” patterns. What are these bands called?
2.	State Nyquist’s Theorem (the “sampling theorem”) in general terms. Exact precision is not required, since it is a fairly difficult theorem. Come as close as you can.
3.	Write the two’s complement representation of −1 using two bytes. Circle your answer. Then show that adding 1 to this value really does give 0. What happens to the carry?

Part II. Computation. Please show adequate work. After you have computed an answer for all the questions, you may use Mr. Hansen’s computer to check your answers.

4.	Convert the following bitstream to (a) big-endian hex and (b) little-endian hex using 16-bit words: 1101010100111101101001101110101001011001011010101010110011001011
(a)
(b)
5.	Perform the following additions in hex, showing work. Then reinterpret your answer in DECIMAL and circle it. If an error condition occurs, be sure to say so. 0BCD +0994 ————— 68F8 +628A —————
6.	Perform the following hex subtractions using two’s complement arithmetic, showing enough work so that it is clear that you know what you are doing. You may check your answer using borrowing and regrouping, of course. If your answer represents a negative number, be sure to indicate that. Then reinterpret your final answer as a decimal number using conventional human notation.
	042C −08BF —————
	33B9 −21AC —————

Part III. Bits, Bytes, Hex, Hertz, and Moore’s Law

7.	Suppose that a certain computer capability costs me $32 million to acquire today. Approximately how far in the future will it be before I can acquire the same hardware capability for about $1? Show your work, and write a sentence or two. Estimation is encouraged—I am not looking for an “exact” answer here.
8.	In our class, we define a gigabyte to be ____________________ bytes or ____________________ bits.
9.	How many kilobytes are in a terabyte? Give both an approximate answer and an exact answer. Exponential notation is acceptable.
10.	Mr. Hansen’s old antique laptops have a clock speed of about 2.5 MHz. Modern computers are generally between 2 and 3 GHz in their clock speed. How much faster is this (to the nearest order of magnitude)? [“Order of magnitude” refers to powers of 10.]
11.	What do we mean when we say that a modern computer runs at, say, 3 GHz? What are we talking about, in plain English?

12.	Consider a movie that is to be shot at 24 frames per second, 1000 by 3000 pixels, using a bit depth of 24 bits per sample. Compute the storage requirement (uncompressed) for this movie if the running time is an hour and 40 minutes. Show work.
13.	How many different sound levels (amplitude values) can be represented with a bit depth of 16 bpp for digital audio?
14.	What audio artifact occurs if a large percentage of the sound amplitude values that are sampled are “too high” or “too low” and simply have to be recorded as the highest or lowest numeric values available as the waveform is sampled? _____________
15.	Does a higher sampling rate (in KHz) help to solve the problem in #14? Why or why not?

16.	Explain, in general terms, how it is possible for a car wheel in a TV advertisement to appear to be stationary (or even turning backwards!) when the ad is shot at 30 frames per second. Diagrams may be helpful.
17.	Make a circuit diagram fragment to show the concept of ~[(~A) NOR (~B)]. Then give a truth table proof to show that ~[(~A) NOR (~B)] is equivalent to A NAND B.
	BONUS SECTION
	(1 pt.) In addition to big-endian or little-endian byte order, it is possible to have __________________________________ in some hardware architectures.
	(2 pts.) Explain why Mr. Hansen does not require an exact answer in #7 and, in fact, would be quite irritated if a student produced an “exact” answer.