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W 9/6/06
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First day of class.
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Th 9/7/06
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HW due (4 pts.):
Note: In order to do this
assignment properly, you will need to spend about 30 minutes leafing through the
textbook, glancing at some of the illustrations, and reading the chapter and
section headings.
Send me an e-mail stating which chapters in the textbook you find most
interesting. (We will cover Chapters 1 and 5, plus a subset of the remaining
chapters as determined by your vote. There is too much material to cover in a
single semester.) If there are any other topics you are especially interested
in, please list those also. In your e-mail, remember to begin your subject
line with a double underscore and to sign your name at the end of your
e-mail. I will ignore any e-mail that is missing the proper subject or that
is unsigned. Important: If you have more than one e-mail address, send
your message from the location that you check most frequently.
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F 9/8/06
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HW due (4 pts.): Read §1.2 (pp. 7-14). Brief reading notes are required. Read the HW
guidelines to earn full credit.
Also, if you did not do yesterday’s assignment involving the e-mail, do it
now so that I know that you know how to send a properly formatted and signed
message.
As for your topic preferences, the top 3 vote-getters were nanotechnology
(not in textbook), coding (Chapter 6), and networking (Chapter 8). I will
develop a syllabus based on your preferences, also incorporating pieces of
other chapters that I think are essential and some topics (though probably in
less detail) from last year’s course
outline. Remember, we will start with Chapters 1 and 5.
Also, please note that since I am a musician, we will definitely spend at
least some time on Chapter 2.
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M 9/11/06
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HW due:
Read §1.3; write §1.2 #1-7 all. Note:
In #4 and #5, use hex notation as an intermediary. An example is shown below.
Show your work, but you may check your work using the Windows Calculator
(calc.exe). Please use suffixes (h for hex or d for decimal) to avoid
confusion. The prefix 0x is also sometimes used to denote hex; feel free to
use that if you prefer.
4c. 1001 0001 = 91h = (9 × 16) + (1 × 1) = 144 + 1 = 145d
5c. 42d = (2 · 16) + (10 · 1) = 2Ah = 0010 1010 = 101010 binary
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T 9/12/06
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Challenge HW due (will be graded for effort):
Recall the definition of the AND gate ( ) and the
OR gate ( ) from Friday’s class. Each of these takes two
inputs and produces one output. The AND gate outputs 1 (true) iff both inputs
are 1; any other combination produces 0. With the OR gate, the situation is
turned around, so to speak: OR always produces 1 except in the single case
when both inputs are 0.
We use the symbol · (multiplication) to indicate AND, and the plus sign (+)
to indicate OR.
The following are true facts in binary logic. They are all pretty
straightforward, except for the last one:
0 · 0 = 0
1 · 0 = 0
0 · 1 = 0
1 · 1 = 1
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1
Now here is your challenge: Remember how we talked about the NAND gate last
Friday? (It’s an AND gate followed by an inverter. In other words, 1 NAND 1 =
0, but any other pair of inputs NANDed together will produce 1.) See if you
can produce an ordinary OR gate by linking nothing but NANDs together in a
clever way. You can use as many as you need—but you are not allowed to use
any other type of component except for NAND gates.
For example, here is an attempt that does not
work:
Remember, the goal is to produce something that always produces 1 unless both
inputs are 0. The diagram above fails, as we can verify by considering cases.
Case I (A = 1, B = 1): The first NAND produces 0, which forms one of the
inputs to the second NAND. The other input is 1 (same as B), and 0 NAND 1 =
1. That is OK, since 1 OR 1 = 1.
Case II (A = 1, B = 0): The first NAND produces 1. The second NAND takes that
1 and the 0 (from B) to produce 1. That is OK, since 1 OR 0 = 1.
So far, things are looking promising. However, we still have two more cases
to check.
Case III (A = 0, B = 1): The first NAND produces 1. The second NAND takes
that 1 and the 1 (from B) to produce 0. Darn! We needed a 1, since 0 OR 1 =
1.
There is no point in checking Case IV, but I suppose we could to illustrate a
point:
Case IV (A = 0, B = 0): The first NAND produces 1. The second NAND takes that
1 and the 0 (from B) to produce 1. That is not correct, since 0 OR 0 = 0.
Hmmm. Well, I guess this circuit failed to do the job. Maybe you can rewire
something, or use more NANDs, or something like that, in order to produce the
desired behavior. Good luck!
By the way, the circuit above is not worthless. It has the following truth
table:
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Case #
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Input A
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Input B
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Output
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1
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1
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1
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1
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2
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1
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0
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1
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3
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0
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1
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0
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4
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0
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0
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1
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This behavior, as it turns out, is identical to the mathematical operation A Ü B. In
plain English, “A is true if B is true.” This behavior, called RIMP (reverse
implication), would be useful in certain situations, but it is not the same as
an OR gate, which would show a pattern of “1, 1, 1, 0” in the output column.
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W 9/13/06
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HW due:
Read pp. 23-31, including reading notes; write pp. 21-22 #13, 16, 27. Reading
notes should follow the HW guidelines in order to
earn full credit. If time permits, also try to finish the HW challenge from
yesterday.
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Th 9/14/06
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HW due:
Revisit problem #13c from yesterday’s set, being careful to avoid the “off by
1” error condition. Use the 210 » 103 rule we learned to estimate your
answer in scientific notation. Then, sketch a circuit diagram using any
combination of AND, OR, XOR, or NOT gates in order to implement a NIMP
(negation of implication) functionality. Note:
This is considerably less challenging than the previous HW assignment, but be
sure to verify proper operation.
Brain teasers:
100, 11, 10, 4, 4, ____
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ____
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F 9/15/06
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Since I forgot to post the HW
assignment by 3:00 p.m., there is no additional HW due. (Yippee!) However,
please finish up the previously assigned problems. Thank you.
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M 9/18/06
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HW due:
Read pp. 249-261. Reading notes are required, as always. See the HW guidelines
for proper format.
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T 9/19/06
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HW due:
Write pp. 266-267 #4, 8, 9, 11, 17, 18, 19, and answer the following
question:
In what way is the “black box” concept we discussed in class yesterday related
to the theory of learning? What, if anything, does the concept of “black
boxes” have to do with skill acquisition in areas such as learning to play
chess well, learning to play a musical instrument, learning a new language,
or learning to be skillful in a sport? Write approximately one paragraph.
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W 9/20/06
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HW due:
Read the next several pages (261-265) on the subject of aliasing.
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Th 9/21/06
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HW due:
Write p. 267 #21, 26; read pp. 268-277; write p. 278 #1-6 all.
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F 9/22/06
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HW due:
Read pp. 281-288; write #26 from yesterday, solving by any means that makes
sense to you. Show your work. You can use the ideas we learned yesterday, or
you can strike out in a new direction. If you are unable to solve the
problem, I would expect to see a detailed record of the things you tried and
an analysis of why they failed. However, I am hoping that you can solve this.
Contact me if you need hints.
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M 9/25/06
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HW due: Read
pp. 281-288. Also, on #26 from last week, I will give you some large hints.
Please bring this problem to completion.
Hint #1: Use radian mode on your
calculator. The function y1
= 12 sin(2px · 1000)
will generate a sinusoid of 1000 Hz with voltage peaks at ±12. Plot this in the window [0, .005] ´ [–12, 12]. Transcribe the graph onto your paper,
labeling points on the x and y axes.
Hint #2: With a 2200 Hz sampling
rate, prove that there will be 11 samples in each 5 full cycles of the
sinusoid.
Hint #3: Show that the samples
during the first 5 milliseconds will be taken at time 0, .005/11, .01/11,
etc.
Hint #4: Set up list L1
to hold the x values as follows:
seq(X,X,0,.005,.005/11)®L1 ENTER.
(Note that the ® or “STO” key is located in the lower left corner of your keypad.)
Hint #5: Set up list L2
to hold the sampled values as follows: Y1(L1)®L2 ENTER.
Hint #6: Use the TBLSET and TABLE
features on your calculator, which should have taught to you in algebra or
precalculus, to display the Y1 values. Use a DTbl value of .005/11 so that the x values match the x values in list L1. Then
make a Y2 function that is the same as Y1 except with
something other than 1000 following the 2px. If you are clever, you can find a value so that
the table values for Y1 and Y2 will match precisely.
Hint #7: One such value is 3200.
See if you can find 2 other values that work.
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T 9/26/06
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HW due:
Read pp. 288-289; write pp. 290-295 #1-7, 11, 14, and 15. Note: In #14, assume that the question
is asking about power ratios, which is typical when talking about audio
signals. As explained in the Wikipedia
article on “decibel,” power ratios and sound levels use a different
definition of decibel from the one that is given in your textbook. You will
want to at scan the on-line article to see what that alternate definition is.
In class: Decibels and review.
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W 9/27/06
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Test on Classroom
Discussion and Textbook Chapters 1 and 5. Please see tests 00, 10, 20,
and 30 from last year’s class for
examples of questions. However, please note that those tests include some
topics that we have not covered, and others, such as quantization noise, were
covered this year but not on those tests.
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Th 9/28/06
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HW due: Get
a good night’s sleep. Congratulations on yesterday’s test scores—they look
good so far.
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F 9/29/06
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HW due:
Plan out at least 2 of your 4 teaching units
and be ready to present today. Prepare at least half a page of written notes
for each topic.
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