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MODD / Mr. Hansen |
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.
1.
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Explain, in
general terms, how undersampling of a digital image
can lead to “banding” patterns. What are these bands called?
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2.
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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.
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3.
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State one advantage that two’s complement representations have over
one’s complement.
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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.
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Convert the
following bitstream to (a) big-endian hex and (b)
little-endian hex using 16-bit words:
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(a)
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(b)
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5.
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Perform the
following additions in hex:
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6.
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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.
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0415
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03CC
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Part III. Bits, Bytes, Hex, Hertz, and Moore’s Law
7.
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Suppose that a
certain computer capability costs me $1000 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.
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8.
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In our class,
we define a kilobyte to be ________ bytes or ________ bits.
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9.
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How many
megabytes are in a terabyte? Give both an approximate answer and an exact
answer. Exponential notation is acceptable.
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10.
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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.]
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11.
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What do we
mean when we say that a modern computer runs at, say, 3 GHz? What are we
talking about, in plain English?
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12.
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I wish to
perform digital audio sampling of a 3-minute song using 2-channel stereo, a
bit depth of 16 bits per sample, and a sampling rate of 44.1 KHz. Compute the
data requirement (uncompressed). Show work.
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13.
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How many
different colors can be represented with a bit depth of 8 bpp
for digital imaging?
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14.
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Unless the
palette is carefully optimized in #13 to choose the “best” colors for the
image, the image will almost certainly exhibit what artifact? _____________
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15.
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Does a higher
resolution (megapixel count) help to solve the
problem in #14? Why or why not?
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16.
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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.
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17.
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Make a circuit
diagram fragment to show the concept of (~A) NAND (~B). Then give a truth
table proof to show that (~A) NAND (~B) is equivalent to A OR B.
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