Assignment 1: Bit Twiddling

DUE DATES:

For the “trivia” assignment: noon, Thursday, September 3. 

For the main assignment: 11:59pm, Friday, September 11. 

Email Shuang Zhai if you plan to use any slip days.

Introduction

The purpose of this assignment is to become more familiar with representing and manipulating data as bits.  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. 

You are to work individually on this assignment.  Assignments later in the semester may be done in pairs. 

Getting Started

We are providing you with a skeleton code file and testing utilities.  To obtain these, copy the file /u/cs252/labf20/datalab/datalab-handout.tar to a (protected) directory in which you plan to do your work.  Then type the command:

tar xvf datalab-handout.tar
to the shell.  This will create a directory called "datalab-handout" with fourteen files in it:

The only file you will be modifying and turning in is bits.c.  All other files should be left as-is.  The file btest.c allows you to evaluate the functional correctness of your code.  The file README contains additional documentation about btest.  Use the command:

    make btest 
to generate the test code and run it with the command:
    ./btest 

Looking at the file bits.c you’ll notice a comment block into which you should insert information identifying yourself.  Do this right away so you don’t forget. 

The bits.c file also contains a skeleton for each of the 13 programming puzzles.  Your assignment is to complete each function skeleton using only straightline code (i.e., no loops or conditionals) and a limited number of C arithmetic and logical operators.  Specifically, you are allowed to use only the following eight operators:

 ! ~ & ^ | + << >> 
A few of the functions further restrict this list.  See the comments in bits.c for detailed rules and a discussion of the desired coding style.  Note also that casts and arrays are not allowed, that you may only declare variables of type int, and that you may only initialize variables to values in the range 0L - 255L

Grading

Your code will be compiled with gcc and run and tested on one of the CSUG Linux machines.  Your score will be computed out of a maximum of 67 points based on the following distribution:

(36) Correctness
(26) Performance
based on the number of operators used in each function
(5) Style
based on the TAs’ subjective evaluation of the quality of your solutions and your comments

The 13 puzzles you must solve have been given a difficulty rating between 1 and 4, such that their weighted sum totals to 36.  We will evaluate your functions using the test arguments in btest.c.  You will get full credit for a puzzle if it passes all of the tests performed by btest.c, and no credit otherwise. 

Regarding performance, our main concern at this point in the course is that you 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 function that satisfies the operator limit. 

Finally, we’ve reserved 5 points for a subjective evaluation of the style of your solutions and your commenting.  Your solutions should be as clean and straightforward as possible.  Your comments should be informative, but they need not be extensive. 

Project Details

Part I: Bit Manipulations

Function Description Rating Max Ops
bitXor(x, y) x^y using only ~ and & 1 14
allOddBits(x) Return 1 if all odd-numbered bits in word set to 1 2 12
conditional(x, y, z) Same as x ? y : z 3 16

The table above describes a set of functions that manipulate and count the bits of an int variable.  The “rating” field gives the difficulty rating (and thus the number of points) for the puzzle, and the “max ops” field gives the maximum number of operators you are allowed to use to implement each function. 

Part II: Two’s Complement Arithmetic

Function Description Rating Max Ops
tmin() Return minimum two's complement integer 1 4
isTmax(x) Return 1 if x is the maximum, two's complement number, and 0 otherwise 1 10
negate(x) Return -x 2 5
isAsciiDigit(x) Return 1 if 0x30 <= x <= 0x39 (ASCII codes for characters '0' to '9') 3 15
isLessOrEqual(x, y) If x <= y then return 1, else return 0 3 24
logicalNeg(x) Implement the ! operator, using all of the legal operators except ! 4 12
howManyBits(x) Return the minimum number of bits required to represent x in two's complement 4 90

The table above describes a set of functions that make use of the two’s complement representation of integers.  The “rating” and “max ops” fields have the same meaning as in Part I. 

Part III: Floating Point Operations

Function Description Rating Max Ops
floatScale2(uf) Return bit-level equivalent of 2*f for floating point argument f 4 30
floatFloat2Int(uf) Return bit-level equivalent of expression (int) f for floating point argument f 4 30
floatPower2(x) Return bit-level equivalent of the expression 2.0^x (2.0 raised to the power x) for any 32-bit integer x 4 10

The table above describes a set of functions that operate on the bit-level representations of (single-precision) floating-point numbers.  The “rating” and “max ops” fields have the same meaning as in Part I. 

In this section, you are allowed to use standard control structures (conditionals, loops, and you may use both int and unsigned data types, including arbitrary unsigned and integer constants.  You may not use any unions, structs, or arrays.  Most significantly, you may not use any floating point data types, operations, or contants.

You can use fshow to see what an arbitrary pattern represents as a floating-point number, e.g.

     ./fshow 2080374784 

Advice

You are welcome to do your code development using any system or compiler you choose.  Just make sure that the version you turn in compiles and runs correctly on the CSUG Linux machines.  If it doesn’t compile, we can’t grade it. 

The dlc program, a modified version of an ANSI C compiler, will be used to check your programs for compliance with the coding style rules.  You can also use it to measure the operator counts of your functions.  You can run these tests by executing the command:

       ./dlc -e bits.c 
The program runs only on the CSUG Linux machines. 

Check the file README for documentation on running the btest program.  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, e.g.,

      ./btest -f bitXor 

The driver.pl is a program that uses both btest and dlc. It takes no arguments.

      ./driver.pl 

“Trivia” assignment

Before noon, Thursday, September 3, submit your answers to the following 4 questions using Blackboard:

  1. Run the following program. 

    #include <stdio.h>
    
    int main(int argc, char *argv[]){
        int bitPattern1 = 0x10011001;
        int bitPattern2 = 0x01100110;
        int bitPattern3 = 0xFFFFFFFF;
        int bitPattern4 = 0x00000000;
    
        /* pair 1 */
        printf("bitPattern1 &  bitPattern2 = %x\n", bitPattern1 &  bitPattern2);
        printf("bitPattern1 && bitPattern2 = %x\n", bitPattern1 && bitPattern2);
    
        /* pair 2 */
        printf("bitPattern1 |  bitPattern2 = %x\n", bitPattern1 |  bitPattern2);
        printf("bitPattern1 || bitPattern2 = %x\n", bitPattern1 || bitPattern2);
    
        /* pair 3 */
        printf("bitPattern1 &  bitPattern3 = %x\n", bitPattern1 &  bitPattern3);
        printf("bitPattern1 && bitPattern3 = %x\n", bitPattern1 && bitPattern3);
    
        /* pair 4 */
        printf("bitPattern1 |  bitPattern3 = %x\n", bitPattern1 |  bitPattern3);
        printf("bitPattern1 || bitPattern3 = %x\n", bitPattern1 || bitPattern3);
    
        /* pair 5 */
        printf("bitPattern2 &  bitPattern4 = %x\n", bitPattern2 &  bitPattern4);
        printf("bitPattern2 && bitPattern4 = %x\n", bitPattern2 && bitPattern4);
    
        /* pair 6 */
        printf("bitPattern2 |  bitPattern4 = %x\n", bitPattern2 |  bitPattern4);
        printf("bitPattern2 || bitPattern4 = %x\n", bitPattern2 || bitPattern4);
    
        return 0;
    } 

    Write the values of the four bitpatterns in binary notation.
    Why do the two outputs differ for pairs 1, 2, 3, 4, and 6? 

    Why are the two outputs the same for pair 5? 

  2. What is the output when the following program runs on a CSUG Linux machine?  Why would the output be different if the program were run on a PowerPC Macintosh? 

    #include <stdio.h>
    int main(int argc, char *argv[]){
        int *translation;
        char bytearray[4];
    
        bytearray[0] = 0x00;
        bytearray[1] = 0x00;
        bytearray[2] = 0xFF;
        bytearray[3] = 0xFF;
    
        translation = (int*) &bytearray;
        printf("Bit pattern = %d.\n", *translation);
        return 0;
    } 

  3. How many lines long is the original bits.c file? 

  4. What is the last line btest prints when compiled and run with the original bits.c file? 

What/how to turn in

The “trivia” assignment will be submitted via Blackboard.  The main assignment will be submitted via the csug.rochester.edu machines using the commad below (make sure you are in the directory that contains bits.c):

    /u/cs252/bin/TURN_IN . 
Watch the Blackboard discussion group for details, and for any clarifications or revisions to the assignment. 

Before running the TURNIN script, be sure that you have