15110 Fall 2012 [Touretzky/Kaynar]
Written Homework 1 - due Friday, September 7 in class
Read sections 1.1-1.2 of chapter 1 of the textbook Explorations in Computing
and read chapter 1 of the book Blown To Bits.
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, lab section (A-N), and the assignment number.
You must hand in your homework at the start of class on the due date
Exercises (10 points total)
(1 pt) Below are pictures of a Chinese abacus (suanpan) and a Japanese
abacus (soroban). Why does the Chinese abacus have two heaven beads
and 5 earth beads in each column, while the Japanese abacus has one
heaven bead and 4 earth beads? Hint: Google is your friend.
Chinese abacus (suanpan)
Japanese abacus (soroban)
(1 pt) Babbage's Difference Engine utilized the method of finite
differences to compute the values of a polynomial function. Suppose
Babbage computes the values of the function and all of its difference
functions for x=0 and puts these into the machine, as shown
below. What does the machine compute for f(1), f(2), f(3) and f(4)
when the handle is cranked?
f(0) = 2
Δf(0) = 4
Δ2f(0) = 26
Δ3f(0) = 18
Charles Babbage wants to compute all of the function values for
the polynomial f(x) = 2x2 + 2x + 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.)
What was the purpose of each of the following computational machines?
And why was each machine desperately needed?
Herman Hollerith's tabulating machine
(2 pts) Punched cards have been used to encode data for tabulating and
computing machines for nearly a century. A standard IBM 80-column
punched card is shown below.
- How many rows does a standard punched card have?
- You can decode a punched card using
the key shown in one of the slides from the first lecture. Notice that the letters A and J
both contain a punch in row 1. What distinguishes an A from a J?
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?
An electronic device has 512GB of memory.
It is connected to a communication port that receives
data at a rate of 16Mbps. How long will it take to
fill up the memory of this device if it starts off
empty? Note the lower case b in 16Mbps. It means 16 mega-bits (not bytes) per second.
- (2 pts) Based on your reading of Chapter 1 of Blown To Bits,
answer the following questions.
- Suppose you have created a work of art that is stored digitally, that is, using bits. What makes possessing those bits different from possessing other types of property such as a painting that you hang on your wall?
- Explain what it means for something to grow exponentially and why it is important as a measure of rate of change.
Give an example from the book about a type of exponential growth that had great impact on computing. (HINT: Think what happened to the speed of processors since the 60s.)
- To what extent can we assume that the world's people are interconnected without any borders? Do national and state borders still matter? Give examples from the book. You can use examples from other sources provided that you give a reference to that source.
Why has outsourcing customer service calls become a common bussiness practice?