Exercise 1: Representing Negative Numbers
1) Start the "Negative binary numbers" applet.
a. Type in -1 and press Return. Study the result. Find the "sign bit". How does the applet indicate it? Come up with a theory of how the sign bit is indicated/ what the rule is for determining which bit is the sign bit. Try and test your theory to be sure. See if you can prove and/or disprove it. Write down your theory of how the sign bit is indicated:
b. Change the number of bits to 32 in the text field "Number of digits in binary" and convert -1 again. Write down how the two forms of binary -1 are different in 32 bits compared to 8 bits. (Feel free to convert -1 into 8 bits again to see the different forms.)
2)
a. Fill in the table you made with the binary values for these two numbers (6 and -6), changing the number of bits from 8 to 12, then to 16, and then to 32.
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6
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6-
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8 bits
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12 bits
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16 bits
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32 bits
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b. Without using the applet, guess what -1 and -6 would look like using 16 bits. Write down your guess.
-1:
-6:
c. Change the number size back to 8 bits. Type in 127 and press Return. Describe what you see below.
3) Now type in -67 to the "Negative binary numbers" applet and convert. Write down the values. What is the difference between +67 and -67 in 2's complement form?
4) Type 4 into the "number of digits in binary" field. Then convert the number 8. What do you see? Does this seem right?
(Pick one)
That seems right to me.
That seems not right to me.
Write down your reasoning:
Exercise 2: Representing Characters
1. Start the "Character codes" applet.
a. Type 100 into the top text area and press Return (or click on the Convert to Character button). Write down what you see.
b. Type in 68 and do the same. What relation does this character have to the first one?
c. Do the same for 101 and 69, and for 102 and 70. Write down the codes and the characters you see.
d. What conclusion can you draw about how upper- and lowercase characters in ASCII are represented, based on your experiments?
(HINT:If you are still stuck, fill out this table.)
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Code
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Letter
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68
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100
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69
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101
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70
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102
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2. If you were writing an algorithm or formula to capitalize text for a word-processing program, what simple mathematical transformation would you make to the character codes to capitalize a letter?
3. Now type in 210, 211, 212, and 213, one at a time.
a. Write down what you see for each one.
210:
211:
212:
213:
b. What characteristics do these characters share?
4. What does ASCII code 241 look like?
Exercise 3: Representing Colors
1. Start the "Color maker" applet.
a. Select Yellow from the names choice pull-down menu. Write down the RGB and HSB values.
RGB:
HSB:
b. Now select Cyan and do the same.
RGB:
HSB:
c. Using more common color names, what color is cyan?
2. Suppose you heard that Kathy's favorite color was 255,0,0. What would Kathy call that color? [TA Note: Please assume that Kathy does not know anything about hex codes, color codes, or even computers at all. Also she speaks American English as her primary language. What would such a person call this color in vernacular American English?]
3. Pick a color from the pull-down list of names in the center, and gradually slide the saturation scrollbar toward the top so that the value in the box below "Sat" goes down to 0. What color do you end up with? Is this true of any color?
Color:
Yeah that should happen for any color.
No that won't happen for other colors.
4. Pick another color from the pull-down list and gradually slide the brightness scrollbar toward 0. What color do you end up with? Is this true of any color?
Color:
Yeah that should happen for any color.
No that won't happen for other colors. If No, what exception(s) did you find?
Exception(s):
5. Page 78 of your textbook gives several color names that are not in the pull-down list. Let's see what maroon looks like. Type 140 into the Red box and press return. Then type 0 into the green box and press return, and do the same for the blue box. Take a screenshot of the applet, and paste it here, below this line: