CS2400 Lab 1- Manipulating Bits Solution

Introduction
The purpose of this assignment is to become more familiar with bit-level representations of integers (and floating point) numbers. You'll do this by solving a series of programming ``puzzles.'' Many of these puzzles are quite artificial, but you'll find yourself thinking much more about bits in working your way through them.
Logistics
All handins are electronic. Clarifications and corrections will be posted on the course Moodle page. Grading will be done through interviews.
Handout Instructions
Start by copying datalab-handout.tar to a (protected) directory on a Linux machine in which you plan to do your work. We recommend the desktop or home directory of your virtual machine. Then give the command unix> tar xvf datalab-handout.tar. This will cause a number of files to be unpacked in the directory. The only file you will be modifying and turning in is bits.c.
The bits.c file contains a skeleton for each of the programming puzzles. Your assignment is to complete each function skeleton. You should should not use loops or conditionals and you can only use a limited number of C arithmetic and logical operators as specified in each problem.
Specifically, you are only allowed to use the following eight operators: ! ~ & ^ | + << >> A few of the functions further restrict this list. Also, you are not allowed to use any constants longer than 8 bits, but you can construct larger constants using 8 bit constants and operators. See the comments in bits.c for detailed rules and a discussion of the desired coding style.
The Puzzles
This section describes the puzzles that you will be solving in bits.c.
Some of the puzzle are bit manipulations (treating the data as a vector of bits), some are focused on two's complement arithmetic, treating bits as numbers. There are some extra credit problems that treat the bits as floating point numbers.
Floating-Point Operations
Functions must handle the full range of possible argument values, including not-a-number (NaN) and infinity. The IEEE standard does not specify precisely how to handle NaN's, and the IA32 behavior is a bit obscure. We will follow a convention that for any function returning a NaN value, it will return the one with bit representation 0x7FC00000.
The included program fshow helps you understand the structure of floating point numbers. To compile fshow, switch to the handout directory and type: unix> make You can use fshow to see what an arbitrary pattern represents as a floating-point number: ``` unix> ./fshow 2080374784
Floating point value 2.658455992e+36 Bit Representation 0x7c000000, sign = 0, exponent = f8, fraction = 000000 Normalized. 1.0000000000 X 2^(121) `` You can also givefshow` hexadecimal and floating point values, and it will decipher their bit structure.
Evaluation
This section only includes evaluation for the standard section, not the extra credit.
The assignment is scored in two parts - you will receive 40 percent of the overall score for having correctly functioning functions handed in on time and 60 percent for being able to correctly explain how your functions work in your interview grading section and how to generalize those solutions.
To compute the 40% for the correctness score, your correctness score will be computed out of a maximum of 53 points based on the following distribution: * 29 of 53 points for correct output * 24 of 53 points for not exceeding the maximum operations
Correctness points
The puzzles you must solve have been given a difficulty rating between 1 and 4, such that their weighted sum totals to 29. We will evaluate your functions using the btest program, which is described in the next section.
You will get full credit for a puzzle if it passes all of the tests performed by btest, and no credit otherwise.
Performance points
Our main concern at this point in the course is that you can get the right answer. However, we want to instill in you a sense of keeping things as short and simple as you can. Furthermore, some of the puzzles can be solved by brute force, but we want you to be more clever. Thus, for each function we've established a maximum number of operators that you are allowed to use for each function. This limit is very generous and is designed only to catch egregiously inefficient solutions. You will receive two points for each correct function that satisfies the operator limit.
Extra Credit
You can receive up to 10% extra credit (for the whole assignment) by completing all of the floating point problems. You will have to read ahead to learn about floating point, because we're going to cover it later; however, you're going to have to learn it someday...
Autograding your work
We have included some autograding tools in the handout directory --- btest, dlc, and driver.pl --- to help you check the correctness of your work.
Note that the autograding script produces a report about 'points' -- this doesn't align with what we've described above (which is what holds). This happens in part because of the presence of the extra problems.
btest
This program checks the functional correctness of the functions in bits.c. To build and use it, type the following two commands:
unix> make unix> ./btest
Notice that you must rebuild btest each time you modify your bits.c file.
You'll find it helpful to work through the functions one at a time, testing each one as you go. You can use the -f flag to instruct btest to test only a single function: unix> ./btest -f bitOr You can feed it specific function arguments using the option flags -1, -2, and -3. For example, the following specifies the first argument is 7 and the second is 0xf. unix> ./btest -f bitOr -1 7 -2 0xf Check the file README for documentation on running the btest program. dlc
dlc is a modified version of an ANSI C89 compiler from that you can use to check for compliance with the coding rules for each puzzle. The typical usage is:
unix> ./dlc bits.c
The program runs silently unless it detects a problem, such as an illegal operator, too many operators, or forbidden code (if, while, etc) code in the integer puzzles. Running with the -e switch: unix> ./dlc -e bits.c causes dlc to print counts of the number of operators used by each function. Type ./dlc -help for a list of command line options.
driver.pl
This is a driver program that uses btest and dlc to compute the correctness and performance points for your solution. It takes no arguments:
unix> ./driver.pl
Handin Instructions
Advice
The dlc program only understands the C89 standard and thus enforces a stricter form of C declarations than is the case for C++ or that is enforced by gcc. In particular, any declaration must appear in a block (what you enclose in curly braces) before any statement that is not a declaration. For example, it will complain about the following code:
int foo(int x) { int a = x; a *= 3; /* Statement that is not a declaration */ int b = a; /* ERROR: Declaration not allowed here */ b *= a; // ERROR -- this comment style causes error
The ``Beat the Prof'' Contest
To submit your entry to the contest, type: unix> ./driver.pl -u ``Your Nickname'' Nicknames are limited to 35 characters and can contain alphanumerics, apostrophes, commas, periods, dashes, underscores, and ampersands. You can submit as often as you like. Your most recent submission will appear on a real-time scoreboard, identified only by your nickname. You can view the scoreboard by pointing your browser at http://cs2400.cs.colorado.edu:8080.