16 Lecture More Selection and Data Representation
Engineering 101
Prof. Michael Falk University of Michigan, College of Engineering
Announcements
Project 3 written part due in lab by today. Project 4 now posted, due Friday 10/20, 7pm Office Hours next week:
Tuesday 7-9pm Pierpont B519 (JL) Wednesday 11:30-12:30 Pierpont (MF) 4-5 CSE2636 (MF) 6-9 UGLi (CO) 6:30-8:30 Pierpont (JL) Thursday 3:30-5:30 Pierpont (JL) 6-9 UGLi (ML) 7-9 CTools Chat (CO) Friday 11:30-12:30 Pierpont (MF) 5-7 Pierpont (CO) 4-7 CTools Chat (ML)
Announcements
Grades to be posted later today. If you notice any discrepancies with Project or Exam grades please report them to your GSI and have them correct the issue. If you notice discrepancies with the PRS contact me. Corrections may take a week or so.
Announcements
Midterm student evaluation site open until October 23 Please let me know what you think is good or bad about the course. To complete an evaluation:
1. Go to http://www.engin.umich.edu/midtermevals 2. Click on the link "Submit Midterm Evaluations"
3. Login (authenticate)
4. At this point, a list of your CoE courses will
appear and you will be able to complete a midterm course evaluation for any/all of them.
Build Your Own Carbon Nanotube
Project 4:
First observed in 1991, carbon nanotubes are one of the linchpins of nanotechnology research. They consist of a graphitic sheet rolled up into a tube.
Build Your Own Carbon Nanotube
Project 4:
There are a countable, but infinite number of ways to construct nanotubes. Each nanotube type is denoted by two positive integers n and m such that n>=m. The value of n and m determine if the tube acts like a metal or a semiconductor. When m=0 the tube is zig-zag, and when m=n it is armchair. Otherwise it is chiral. In this diagram Ch is the direction that will be rolled up and T is the direction of the tube axis.
Build Your Own Carbon Nanotube
Project 4:
To construct the vector Ch, we hop n times in the a1 direction and m times in the a2 direction. Ch = n a1 + m a2 Your job will be do make a program that 1. Makes a rectangle of carbon sheet described by the numbers n and m and a third number l that gives the length of T. 2. Makes a carbon nanotube from this same sheet by rolling it up.
Build Your Own Carbon Nanotube
Project 4:
I have provided both a working version of the code and a visualization program that you can use in MATLAB. Copy the file atomsplot.m into your Project4 directory. Make sure MATLAB is pointed to the correct directory. Simply import your data and type atomsplot(sheet, 0.2) to plot the tube. (0.2= atom size) Use the Camera Toolbar to view. Make sure to test zig-zag, chiral and armchair tubes.
Which procedure will....
Request a single integer number. It then asks the user to input a number. If the number guessed is too high print out "guess lower" and get another number If the number guessed is too low print out "guess higher" and get another number If the number guessed is correct let the user know this is the number and tell how many times the user had to guess.
Guessing Game
void GuessIt (int n){ int guess, num=1; cout << "guess a number" << endl; cin >> guess; while ( guess != n ){ if ( guess > n ) cout << "Guess lower" << endl; else cout << "Guess higher" << endl; cin >> guess; num = num + 1; } cout << " You guessed it in " << num << " tries" << endl; return; }
Using Selection To Check Program Status
One of the most important uses of selection is to check the status of a command or action
cout << "Enter a positive number" << endl; cin >> n; exit() is if (n <= 0){ defined in the cout << n << " is not positive" << endl; cstdlib library. exit(EXIT_FAILURE); It terminates } the program. cout << "The square inverse root is " << 1.0/sqrt(static_cast<double>(n))<<endl;
Using Selection To Check Program Status
Streams are a particular case in point since whenever you try to open or read from a file you don't know if the file might not exist or be finished.
stream.fail() can be used with any stream ifstream infile("myfile.data"); and returns true if the last action failed. if( infile.fail() ){
cerr << "Problem with file" << endl; exit(EXIT_FAILURE); } infile >> x >> y >> z;
fail() can also be used to read files of arbitrary length
int x, n=0; ifstream infile("myfile.data"); infile >> x; while (! infile.fail() ){ cout << x; n = n + 1; infile >> x; } cout << "read in " << n << " integers." << endl;
Switch Statements
A switch statement is used to decide between a number of cases
switch (integer_expression){ case value: expression case value: expression default: expression }
The integer expression is evaluated and the thread of execution starts from the matching case. If none matches it starts from the default.
Switch Statements
switch (weekday){ case 1: cout << "Monday"; break; case 2: cout << "Tuesday"; break; case 3: cout << "Wednesday"; break; case 4: cout << "Thursday"; break; case 5: cout << "Friday"; break; default: cout << "Weekend"; }
breaks are needed. Otherwise switch drops through to next expression.
Two Important Halves of Computer Programming
Execution Control
Sequence Selection
Iteration
Data Representation
How do we structure the data that we are
acting on?
Data Representation
All data inside the computer is represented by bits. Bits can have only two values 0 or 1. 4 bits make a nybble 8 bits make a byte 11001010 10101011
Data Encoding
Bytes
11001110 10101010 11110000 10100101 11111111 11001110 11001110
Meaning
Hail! to the victors valiant Hail! Hail!
How many things can you encode with a byte (8 bits)?
Each bit allows two possibilities. 1 bit: 0 1 (2 things) 2 bits: 00 01 10 11 (4 things) 3 bits: 000 001 010 011 100 101 110 111 (8 things) n bits: 2n things 8 bits: 256 things
Base 2 is a number system like base 10
456,347
Base 2 is a number system like base 10
456,347
100000 10000 1000 105 104 103 4 5 6 100 102 3 10 101 4 1 100 7
Base 2 is a number system like base 10
456,347 100000 10000 1000 105 104 103 4 5 6 100 102 3 10 101 4 1 100 7
4 x 105 + 5 x 104 + 6 x 103 + 3 x 102 + 4 x 101 + 7 x 100
Base 2 is a number system like base 10
110001 32 25 1 16 24 1 8 23 0 4 22 0 2 21 0 1 20 1
1 x 25 + 1 x 24 + 0 x 23 + 0 x 22 + 0 x 21 + 1 x 20
Base 2 is a number system like base 10
110001 32 25 1 16 24 1 8 23 0 4 22 0 2 21 0 1 20 1
1 x 25 + 1 x 24 + 0 x 23 + 0 x 22 + 0 x 21 + 1 x 20 110001(base 2) = 32+16+1 = 49(base 10)
Convert the Binary Number to Decimal
128 27 64 26 32 25 16 24 8 23 4 22 2 21 1 20
01000001
1- 27 2-65
3- 67 4-79
Convert the Binary Number to Decimal
128 27 64 26 32 25 16 24 8 23 4 22 2 21 1 20
01000001 65
Convert the Binary Number to Decimal
128 27 64 26 32 25 16 24 8 23 4 22 2 21 1 20
01101011
1- 85 2-101
3- 97 4-107
Convert the Binary Number to Decimal
128 27 64 26 32 25 16 24 8 23 4 22 2 21 1 20
01101011 107
Adding Binary Numbers
+
01100 00110
Adding Binary Numbers
+
01100 00110 0
numbers are added column by column
Adding Binary Numbers
+
01100 00110 10
numbers are added column by column
Adding Binary Numbers
+
01100 00110 210
2 is not a valid binary digit.
In this case recall that 10 in binary equals 2 in decimal
Adding Binary Numbers 1 01100 00110 010
+
So we replace the 2 by a 0 and carry the extra 1.
Adding Binary Numbers 11 01100 00110 0010
+
So we replace the 2 by a 0 and carry the extra 1.
Adding Binary Numbers 11 01100 00110 10010
+
So we replace the 2 by a 0 and carry the extra 1.