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1) Convert the binary number 10110101 to decimal by hand, showing
all steps. Use the scrap paper provided by the TF. Write the final
result here, i.e. the decimal representation.
2) Using the “Number systems” applet, type 10110101 into the Base
X text area. Verify your answer above. Take a screenshot (press the
key “PrtSc”) and paste (Ctrl-V) it here.
3) One way to convert a decimal number to binary is to repeatedly
divide the number by 2, writing down the remainder at each step.
(See page 43 of your textbook for an example that does this using
hexadecimal, or base 16, instead of binary). To see how to do this in
binary, type a number, such as 42, into the Base 10 text area of the
“Number Systems” applet and press Convert. The steps are shown in
the little pink window that pops up. (Nothing to write here)
4) To learn how to do this yourself, convert the decimal number 51 to
binary using this method of repeated division, just like the applet did.
Use the scrap paper provided by the TF. Write the final result here,
i.e. the binary representation.
5) Use the “Number systems” applet to check your result. Type 51
into the Base 10 text area and press Convert. Take a screenshot and
paste it here.
6) Use the “Number systems” applet to convert 121 from base 5 to
decimal. Type 121 into the Base X text area, select Base 5 from the
choices in the pull-down menu, and click Convert. Does this make
sense to you? Why? Take a screenshot and write on the paper why
121 (base 5) equals whatever the applet shows you. (Review page
36 of the textbook for an explanation).
7) Add the two binary numbers together by hand, showing all carries:
01101101
+ 10001011
Use the scrap paper provided by the TF. Write the final result here.
8) Now type the numbers 01101101 and 10001011 into the Binary
column of the “Binary addition” applet. Click on Add and verify your
answer with the applet’s result. Take a screenshot.
9) Use the “Binary addition” applet to add the numbers 01101101 and
10101011 instead (note that only 1 bit has changed). What
happened to the leftmost bit in the addition?
9 cont.) What are the limits of the “Binary addition” applet? What are
the largest numbers it can add? What is the largest result it can
produce? Record your answers below, in both binary and decimal
values.
Largest numbers it can add:
Largest result it can produce:
10) We can use the addition applet to perform subtraction. This is
done by adding a negative number. We will use 2s complement to
represent the negative numbers. Now try 5 – 3, first with paper and
pen, then paste a screenshot of the applet verifying your answer. Do
the same for 3 – 5.
11) List the ASCII representations of the following characters:
•
•
•
•
•
•
•
a
A
z
Z
0
9
10
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___
___
___
___
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Do you see any pattern in the ASCII encoding scheme? If so, what is
it?"