This lab is to be done alone (no partners). The assignment includes a written part that you will hand in at the beginning of lab on Wednesday and the programming part that you will submit electronically by Tuesday evening (detailed submission instructions below).

Lab 1 Goals:

• To understand binary data representation of different types: int, unsigned, float, char
• To be able to convert between decimal, binary and hexadecimal representations
• To understand Binary arithmetic and apply it
• To understand bit-wise operations, and to use C bit-wise operators to manipulate binary data
• Practice with basic C programing and gdb

You will use git for managing lab starting point code distribution, for submitting your lab solutions, and in subsequent labs for sharing code with your partner.

For each lab assignment you will start by creating a local copy (clone) of a remote git repo that contains starting point code for the lab. A summary of the basic steps for doing this are:

1. Get the ssh-URL to your Lab 1 git repository from the GitHub server for our class: CS31-f15
2. Using your URL, and from your cs31/labs/ subdirecory, run git clone to clone a local copy of your repo:

     cd ~you/cs31/labs/
     git clone [your-ssh-URL]
   

We are going to do this together in more detail:

1. If you have not already done so, create a cs31/labs subdirectory into which you will clone your git repo containing your lab 1 starting point code:

     cd
     cd cs31
     mkdir labs
     cd labs
     pwd           # should be /home/you/cs31/labs/
   

2. Next, clone your Lab1 repo into your labs subdirectory. To do this we will step through the directions for "Setup for using repos on Swarthmore's GitHub Enterprise" on my using git page. You should have already completed the one-time set-up steps for Lab 0, but if not do that first: One-time configuration for using Swarthmore GitHub Enterprise

3. At this point you can cd into your local repo and start writing, compiling, and testing your lab 1 solution code:

   cd ~you/cs31/labs/Lab1
   ls
     Makefile README.md lab1.c 
   vim README.md
   vim lab1.c
   make
   ./lab1
   

Read over the Git Overview and the sequence of git commands for using git to add, commit and push your code changes to the master repo:

git add lab1.c
git commit
git push    # to also push changes to your master repo

This part of the lab is a written assignment. You can either write-up your solutions by hand or write them up in vim (or emacs) and print the resulting file to one of our printers. To print a file created by vim (or emacs) on a CS lab printer use either enscript or lpr:

$ lpr filename
$ enscript -2rG filename

If you write up your answers in vim (or emacs) make sure to not have lines longer than 80 characters (explicitly hit the Enter key to start a new line). If you have lines longer than 80 characters they will either be cut off by the printer or wrapped strangely. One way to ensure this is to work in a terminal 80 characters wide when you run vim so you can see when the currently line is too long and starts to wrap around. Typing in CNTRL-L in your file will print a page break:

hello1     # this will print on the first page
^L         # this is typed in using CNTRL-L 
hello2     # this will print on the second page

For these problems you are graded on showing how you applied the operation or conversion method we described in class: you must show your work or explain how you got the result to receive credit. Check your answers for correctness by either writing a C program to do some of the computation and printing result values or by using gdb's print command. See the weekly lab page for details on using gdb.

Answer the questions below showing your work and/or explaining your answer. For these questions, if a question specifies a number of bits, your answer should be in a corresponding number of digits. For example, if the question asks to add 4 bit values together your answer should be a 4 bit value not a 64 bit one. Also, assume that for signed values, the high-order bit is the sign bit. For example, 1000 should be interpreted as negative as a 4-bit signed value, but positive as an 8-bit signed value (00001000).

1. What is the largest positive value that can be represented with a 2's complement 8 bit number? Explain.
2. What is the largest positive value that can be represented with an unsigned 8 bit number? Explain.
3. convert the unsigned 8 bit binary value 10100110 to decimal. Show your work.
4. convert the signed 8 bit binary value 10100110 to decimal. Show your work.
5. For the following 8 bit binary values (show your work):

   value 1: 01011101
   value 2: 01100101
   

   1. What is the binary representation of the result of adding them together as unsigned 8 bit values? Does this operation result in overflow? If so, when?
   2. What is the decimal representation of the resulting addition if the two values are unsigned 8 bit values?
   3. What is the decimal representation of the resulting addition if the two values are signed 8 bit values?
   4. What is the binary representation of the result of subtracting the second from the first as unsigned 8 bit values? Does this operation result in overflow? If so, when?
6. Convert the following 2 byte binary numbers to hexadecimal, indicating how each part is converted (the binary values are shown with spaces between each 4 digits just to make them easier to read):
   1. 0000 0110 0001 1111
   2. 1100 0101 1110 0101
   3. 1010 0111 1101 0110
7. Convert the following hexadecimal numbers to binary, indicating how you converted each digit:
   1. 0x23
   2. 0x852
   3. 0xc1a6
   4. 0xefab
8. Convert the following decimal values to 8 bit binary and to hexadecimal. Show your work:
   1. 12
   2. -36
   3. 123
   4. -123
9. Given the following 4 bit binary values, show the results of each bit-wise operation, showing both the binary and decimal result value for each (list the unsigned decimal value):
   1. 0110 | ~(1010)
   2. ~(0110 | 1010)
   3. 0111 & ~(1001)
   4. (1010 | 0000) & 1111
   5. 0011 ^ 1110
   6. 0111 << 2
   7. 0111 >> 2

You will write a single C program that when run, prints out answers to each of the questions below. For each question, print out a string that is your answer to the question, and then print out some expressions and their results that support your answer to the question. For example, the beginning of a run of your program might look like this:

$ ./lab1
Question 1: my answer to question 1 is ...
    This can be verified by examining the result of the expression ...
    when x is the int value ... and y is ... the expression is ... 
    when x is ... and y is ... the expression is ...

Question 2: my answer to question 2 is ...
    This can be verified by ...

Each answer should include printing out the value(s) of COMPUTATION(s) that demonstrates your answer's correctness. DON'T just print something like this:

   printf("The answer to question 1, what 0x2 + 0x6, is 0x8\n");

Instead, have C code that computes the answer to show or to prove that your answer is correct:

   unsigned x, y, z;
   x = 0x2; y = 0x6;
   z = x+y;
   printf("The answer to question 1, what %x + %x is %x\n", x, y, z);

For some questions, the code proving your answer correct may be as simple as the example above. For others, however, you will have to think about how to constructing some arithmetic expressions that will demonstrate the correctness of your answer.

You may want to try printing some values and expressions in gdb in binary, hexadecimal, and decimal to help you figure out good values to test in your C program to ensure you considering all cases.

Answer these questions by writing a C program that prints out the answer and prints out example expression(s) that support your answer

1. Given the following variable declaration and initialization, how many ways can printf display the value of x? Show all of them.

   unsigned int x;
   x = 97;
   

2. What is the maximum positive value that can be stored in a C int variable? (write code that both gives the answer and proves/demonstrates your answer is correct)
3. What is the maximum value that can be stored in a C unsigned int variable?
4. What arithmetic operation is equivalent to left shifting an unsigned int value by 1?
5. What arithmetic operation is equivalent to left shifting an unsigned int value by 2?
6. What arithmetic operation is equivalent to right shifting an unsigned int value by 1?

Hints and Requirements for this part

• The answer to each question should be implemented as a separate function called by main. For example, main might look like:

  int main() {
    question1();  // call the question1 function
    question2();
    ...
  

  And, you are welcome to add additional helper functions.
• Each answer should contain enough examples to support it. If your answer is "false", this usually means just providing a single counterexample that proves the statement false. If your answer is "true", then find a few different cases that demonstrate your claim. Do not, for example, enumerate every possible int value. For most questions, it should be enough to have 4 or 5 examples to support your answer. Do not have more than 10 for any one question.
• Examples in support of your answer must be computed by the C program. For example, don't just print out the string "3 + 6 = 9" instead write C code that computes the expression and prints out its result, like this:

    int x, y;
    x = 3;
    y = 6;
    printf ("%d + %d = %d\n", x, y, (x+y));
  

• Your C program, when run, should print out the answer to each question in order, with supporting examples, in an easy to read format. Use formatted printf statements, and do not print out lines that are longer than 80 characters (break long output up into multiple lines). Look at printf examples and documentation to use nice formatting for any tabular output your program might produce.
• Remember that type is important in C, and that if you use different formatting strings to printf, you can print out the same value as different types (for example, if you print out a value using %u you may see a very different value that if you print it out using %d). If you are not seeing the values that you expect to see, check your printf format string and use gdb to examine your running program.
• You should use good C programming style. See my C Style Guide for examples of commenting code and avoiding line-wrapping.
• For C programming help, refer to the weekly lab examples and see my C programming help/links page.
• Use the Makefile to build your program.

To submit your Lab solutions, you must run three git commands before the due date. To submit your code, simply commit your changes locally using git add and git commit. Then run git push to push your local committed version to the remote master:

  git add lab1.c
  git commit lab1.c  -m "lab1 is done"
  git push

You can run these any number of times before the due date to update your solution answers in the remote master. In fact, this is good practice to solve some of the lab, do and add, commit, and push, then solve more, ...

At the due date I will pull your solutions form the remote master git repo and grade those. I can only see and grade changes to your Lab1 Git Repo that you push. Git will only push changes you commit. Git will only commit things you add.

It is also good practice to not modify your Lab source code (lab.c) after the due date. If something goes wrong, I'll use the modification date of the file in your local repo to determine which version of your solution you submitted before the due date.

Some other information about add, commit, push

You can see if you have any changes from your local latest commit by running git status (this will tell you if you need to add and commit something, and likely push too). For example, in this run of git status, the "Changes not staged for commit" output tells me that I have made changes to lab1.c since my last add and commit, and I need to add, commit, and push them to the repo:

git status
Changes not staged for commit:
  (use "git add ..." to update what will be committed)
  (use "git checkout -- ..." to discard changes in working directory)
        modified:   lab1.c

Also, please never add, commit or push files that can be created from running gcc (i.e. executable files). If you run make clean before running git commands, this will help ensure that you do not by mistake add an executable file to your git repo.