15110 Summer II 2012
[adapted from Cortina/von Ronne]
Written Assignment 1 – due Monday, July 9 at 9 am sharp.
Reading assignment
Read sections 1.1-1.2 of chapter 1 and sections 2.1-2.4 in chapter 2 of the
textbook Explorations in Computing and chapter 1 and pages 19-42 of chapter 2 of the
book Blown To Bits.
Instructions
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Type or neatly write the answers to the following problems.
Please STAPLE your homework before you hand it in.
On the first page of your homework, include your name, andrew ID, date, and the
assignment number. Number your pages.
You must hand in your homework at the start of class on the given due date.
Exercises
1. Babbage's Difference Engine utilized the method of finite differences to compute
the values of a polynomial function. Babbage computes the values of the function
and all of its difference functions for x=0, and these values are given below. What
does the machine compute for f(1), f(2), f(3) and f(4) when the machine is
cranked? (Show all your work.)
f(0) = 7
Δf(0) = 6
Δ2f(0) = 3
Δ3f(0) = 2
2. Charles Babbage wants to compute all of the function values for the polynomial
f(x) = 3x2 + 6x + 7 for x = 1 to 1000. Using the method of finite differences, what
initial values does he set his machine to if he wants it to start at x = 0? (HINT:
You'll need to compute the difference (delta) functions first.)
3. What was the purpose of each of the following computational machines? Why
was each machine desperately needed?
a. Herman Hollerith's tabulating machine
b. ENIAC
4.
a. An electronic device has 128GB of memory. It is connected to a
communication port that receives data at a rate of 256Mbps. How long will
it take to fill up the memory of this device if it starts off as empty?
b. Moore's Law states that the processing power of a computer doubles
approximately every 2 years. Based on this observation, how many years
will it take to have a computer that is approximately a thousand times
more powerful than today's computer?
5. For each of the following Ruby expressions, show how they are evaluated by
evaluating one operation at a time and showing the reduced expression until
you have a final answer. For example, if the Ruby expression is 3 * 4 + 5, you
answer would look like this:
3 * 4 + 5
12 + 5
17
HINT: Check your final answers with irb!!!
a.
b.
c.
d.
(11 - 9 + 10) / (4 + 1 ** 2)
2 ** 2 ** 2 ** 2
15100 % 2000 % 300 % 45 % 25
18 * 4+5 / 5-2
6. For each of the following invalid Ruby expressions, run them in irb and explain
the errors that you see.
a.
b.
c.
d.
Math.sqrt(-100)
11 % 0
end = "Friday"
"15000" + 110
7. Consider the following Ruby method that returns the body mass index (BMI) of
an individual given the person's height in inches and weight in pounds.
def compute_bmi(height, weight)
return weight * 703 / height ** 2
end
a. Suppose Alice has a height of 63 inches and a weight of 132 pounds. If we
call this function to compute her BMI as follows:
compute_bmi(63, 132)
will we get an integer result or a floating point result? Why?
b. Suppose Bob has a height of 72 inches and a weight of 180 pounds, but we
call this function with these values mixed up:
compute_bmi(180, 72)
Does Ruby report an error? Why or why not?
c. Suppose we only know that Carol's height is 65 inches, and we try to compute
her BMI as follows:
compute_bmi(65)
Does a default weight get used in our function or does Ruby complain about
this function call? Explain.
d. Suppose we replace the return statement with a print statement as shown
below:
def compute_bmi(height, weight)
print weight * 703 / height ** 2
end
e. Why does the following computation fail?
average_bmi=(compute_bmi(63,132)+compute_bmi(72,180)+compute_bmi(65,147))/3.0
NOTE: Don't just say how to fix the function. Explain why the computation fails
based on the current function definition.
8. Consider the following Ruby method definition that uses a loop:
def mystery(n)
value = 1
for i in 1..n do
value = value * i
print value
print "\n"
# print a newline character
end
end
a. What does this method display if we call it as follows:
mystery(6)
b. What mathematical function is this Ruby method computing in general if n >
0?
c. Suppose we replace the first instruction inside the loop with the following:
value = value * 2
d. Now what mathematical function is this Ruby method computing if n > 0?
e. Using irb, see what happens in the original function if we replace
the print statements with a return statement instead:
def mystery(n)
value = 1
for i in 1..n do
value = value * i
return value
end
end
Store the function in a file, then load it in irb and call it with different positive
integers and observe the results. What do your observations suggest about how
the return statement works?
9. Based on your reading of Chapter 1 of Blown To Bits, answer the following
questions.
a. A common theme in computing is dealing with advances in technology
that change exponentially. Exponential changes are often hard to see at
first but become very obvious once it's too late to adapt. Give an example
from this chapter of a company that didn't see exponential changes in its
core business, resulting in massive layoffs and a major loss in revenue.
b. Eliot Spitzer, former governor of New York, was forced to resign due to a
prostitution scandal. How was his involvement detected digitally?
c. Years ago, people copied songs on to cassette tapes and shared them
with their friends, yet the recording industry didn't pursue these people for
copyright infringement. Today, however, sending a friend a copyrighted
mp3 file can get you into trouble. Why is the response different now?
d. Once digital data about you is stored, can it be completely erased? Why or
why not?
10. Besides learning how to use computational devices to solve a problem, we
should understand what happens once the device solves the problem for us.
Based on your reading of Chapter 2 (pages 19-42) of Blown To Bits, answer the
following questions about the digital data you generate and how all of this digital
data affects your privacy.
a. Give two examples of how you might leave "digital footprints" while driving
your vehicle, based on what you read in the chapter. (Write 2-3 sentences
for each example you cite.)
b. Briefly describe one example from the reading where a person's
confidential medical records were discovered by linking the anonymized
records with another data set.
c. Identify one example of how stores might digitally track your purchases so
they can suggest new items for you to purchase, based on what you read
in the chapter. (Write 2-3 sentences to explain how the tracking is done.)