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F 10/1/010
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HW due: Read pp. 135-159;
write p. 159 #6. Since this is a lot of reading, you should plan to do part
of it on Wednesday night and part on Thursday night.
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M 10/4/010
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HW due: Read pp. 161-173; write
p. 160 #14-15 and the mini-project below. All homework must conform to the homework guidelines and must be stored in a 3-ring
binder in order to earn full credit.
Mini-Project: Use a digital
photograph in order to create Moire patterns as aliasing artifacts. (Moire
patterns are described on p. 263.) You can use this public domain image of Citigroup
Center in New York City, or you can use any other image you wish, as long
as it has a number of parallel lines in it.
1. Save your image as a .JPG file on your computer’s hard disk.
2. Open your image in Windows Paintbrush or a similar paint program. Note: Do not use a drawing program,
and do not use a presentation program such as PowerPoint. We need something
that will allow us to demonstrate the effect of undersampling.
3. Do you see any curved lines anywhere? _________ (The answer is probably
no.)
4. Reduce the size of your image by a factor of 5. (In Paintbrush, the
commands are Ctrl+A followed by Ctrl+W, then 20 TAB 20 ENTER. This will
create a new image that is 20% the size of the original.)
5. Restore your image to its original size. (In Paintbrush, the commands are
Ctrl+W followed by 500 TAB 500 ENTER.)
6. Do you see any curved lines now? _________ Make an extremely rough sketch
on your homework paper, showing where the curved lines are.
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T 10/5/010
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No class today. (Mr. Hansen
is out sick.)
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W 10/6/010
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No additional written HW is
due. Make sure you are caught up with all previously assigned reading and
problems.
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Th 10/7/010
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HW due: Read pp. 33-46;
write p. 58 #14.
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F 10/8/010
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No school (faculty
professional day).
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M 10/11/010
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No school (holiday).
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T 10/12/010
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HW due: Read pp. 46-63;
write p. 58 #7, 8, 9.
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W 10/13/010
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HW due (Alex): Order your
textbook. Click the archives link on the main MODD class page and look at the
9/9 calendar entry to find the link to the textbook information. Then do the
homework that was due 9/10, read the steganography handout (see 9/27 calendar
entry) and prepare a short list of questions from the topic list below.
HW due (everyone else): Prepare a set of lecture notes (notecards preferred)
from which you can conduct a review session for at least 10 to 15 minutes if
called upon. Karl is exempt from this requirement, since he managed to speak
extemporaneously for longer than that yesterday.
MODD Topic List, 9/8/2010–10/15/2010
210 = 1024
K, M, G, T
bits, bytes, nibbles
binary
hex (incl. arithmetic, endianness, 1’s complement, 2’s complement)
AND, OR, NAND, NOR, XOR, IMP, etc.
digital vs. analog
steganography: “hidden in plain sight”
digital imaging
—“posterization”
—bpp
—halftone
—pixel resolution
—artifacts (esp. Moiré effects)
Hz: KHz = 1000 cycles/sec., MHz = 1 million cycles/sec., etc.
Moore’s Law
relational database = set of tables (where each table has rows for records, cols. for fields)
digital audio
—period
—amplitude
—frequency (reciprocal of period)
—artifacts (clipping, aliasing/undersampling, insufficient
dynamic range)
—sampling rate, Nyquist’s Theorem
—bit depth
block diagrams
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Th 10/14/010
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HW due (Alex): Borrow a
textbook and read Chapters 1, 2, and 3.
HW due (everyone else, including Karl): Prepare 10-12 minutes’ worth of
lecture notes on the topic list above. I recommend choosing at least some
topics that you are not already expert on, so that you can learn as you write
out your notes.
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F 10/15/010
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Test (100 pts.) on all topics discussed so far. The list of topics will be limited to those shown
in the 10/13 calendar entry.
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M 10/18/010
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HW due: Re-do your entire test from last Friday, and record how long
it takes you. You may confer with other students if you wish, but the
learning benefit is greater if you push yourself to do the best possible job
on your own before you break down and call somebody or look in the textbook.
The test may be re-graded for accuracy as a double (or triple) homework
assignment. Grammar, neatness, and legibility count.
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T 10/19/010
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HW due: Correct yesterday’s
assignment and do several additional addition and subtraction problems. Make
up problems that show that you understand the techniques, and show your work.
I would like everyone to have a “check plus” this time (no zeroes, and no
check minuses”). Everyone has at least one or two errors to correct. Remember
the following tips when using two’s complement arithmetic:
(1) Padding with leading zeroes may be required before you start.
(2) If the answer overflows, the lead digit of the overflow is discarded.
(3) If the answer is detected to be negative (because the lead digit without
overflow is 8 or higher), then the answer must be reinterpreted as a negative
number. We do this by taking the two’s complement at the end. (Remember, that
means to take the one’s complement and add 1.)
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W 10/20/010
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HW due: Keep preparing for
your optional retest on Chapters 1-3, but also perform the following addition
and subtraction problems using two-byte two’s complement arithmetic. The
first one has been done for you as an example. Show all of your carries, and
use the Windows Calculator to check your work. Give all answers in “human
notation” as well as hex.
1. 63CC
+73B7
=====
D783, which is an overflow condition since anything 8000h or higher
represents a negative number in two’s complement. The “answer” is found by
complementing D783h to get 287Ch, but then we have to add 1 to get 287Dh. In
decimal, that represents 2(4096) + 8(256) + 7(16) + 13(1) = 10365 with a
negative sign. Final (wrong) answer is −10365 in decimal, and
the answer is wrong because it represents an overflow condition. After all,
we should not be allowed to add two positive numbers to get a negative,
should we?
2. 36FE
+7ABC
=====
3. ADE8
-3416
=====
4. 218A
-46EC
=====
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Th 10/21/010
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Optional Retest (100 pts.) on Chapters 1, 2, and 3.
Since I would like everyone to do well on this test, I am posting a complete answer key to last Thursday’s test.
The retest will, of course, have somewhat different questions.
Also, as promised, here are the solutions to the rest of yesterday’s homework
problems:
111
2. 36FE
+7ABC
=====
B1BA
Now, B1BAh represents a negative number. How do we know? Look at the lead
digit, which is 8 or more, indicating that the sign indicator bit is turned on.
B1BAh represents the negative number found by taking the two’s complement,
namely 4E46h, and converting that to decimal. Answer: 4(4096) + 14(256) +
4(16) + 6(1) = 20038 with a negative, or −20038. Clearly, this
represents an overflow error, since two positive numbers should never add up
to a negative number.
3. ADE8
-3416
=====
Here we have a negative minus a
positive, which should produce a negative result. First, we must rewrite
using two’s complement:
111
ADE8
+CBEA
=====
179D2
Remember that since we added the two’s complement of 3416h, which is
equivalent to subtracting 3416h and
adding 10000h, our answer here is too high by exactly 10000h. Luckily,
subtracting 10000h to correct our answer is a simple matter of discarding the
lead digit. Final answer is 79D2h = 7(4096) + 9(256) + 13(16) + 2 = 31186,
but since that is positive (less
than 8000h) instead of negative, we know that an overflow error has occurred.
That makes sense if you think about it, since ADE8h represents −21016
in decimal, and 3416h represents 13334 in decimal. Thus subtracting gives
−21016 − 13334 = −34350
in decimal. However, −34350 is less than the most negative number that
can be safely expressed in two’s complement, namely 8000h = −32768
decimal.
Therefore, #3 is like a mirror image of #2. Instead having two positives
adding up to equal a negative, we have two negatives adding up to equal a
positive. Either way, we have a sure indication that an overflow has
occurred.
4. 218A
-46EC
=====
This one is much easier than the
others. Since the two’s complement of 46ECh is B914h, we rewrite as
218A
+B914
=====
DA9E
Here, the answer must be interpreted as
negative since the lead digit is 8 or more. Does that make sense? Yes, it
does, since 46ECh > 218Ah, which tells us that the answer when subtracting
should be negative. Great! The
question is, what does the answer represent?
To find the answer, we must take the two’s complement of DA9Eh, namely 2562h,
giving 2(4096) + 5(256) + 6(16) + 2 = 9570 as a negative, or in other words, −9570
decimal.
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F 10/22/010
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HW due: Read pp. 69-81.
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M 10/25/010
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Day off.
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T 10/26/010
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HW due: Read the tan boxes in
the left margin of p. 82 (three paragraphs), the top half of p. 82
(introduction and two numbered paragraphs), the bottom of p. 83 (“Additive
Synthesis”), and pp. 181-194; write p. 195 #10.
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W 10/27/010
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HW due: Read pp. 196-204; write
p. 212 #4, 5, 7.
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Th 10/28/010
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HW due: Read pp. 204-211;
write p. 212 #6 and the two problems below.
19. Rewrite matrix A in #4 in hex
(one byte per entry).
20. Rewrite matrix A in #4 two
different ways using a threshold operation, following the rules of equation
4.5 on p. 207. Give answers in hex. Use these threshold values:
(a) v = 0Bh
(b) v = 1Ah
21. Attempt to increase the contrast in matrix A in #4 by multiplying each entry by 10h (i.e., by the decimal
value 16). Remember to “clip” any entry that exceeds FFh.
22. When the operation in #21 is applied, does the contrast improve
throughout the image or only in certain portions of the image? Explain
briefly.
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F 10/29/010
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End of Q1. All Mathcross puzzles and any other graded
items must be submitted by 3:00 p.m. today.
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