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.
We are providing you with a skeleton code file and testing
utilities. To obtain these, copy the file
/u/cs252/labs/bit-twiddling-handout.tar
to a (protected) directory in which you plan to do your work.
Then type the command:
tar xvf bit-twiddling-handout.tarto the shell. This will cause eight files to be created in your directory:
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 C stucture
team 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 15 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.
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 80 points based on the following distribution:
The 15 puzzles you must solve have been given a difficulty rating
between 1 and 4, such that their weighted sum totals to 39. 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, half
credit if it fails one test, 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 10 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.
| Function | Description | Rating | Max Ops |
|---|---|---|---|
bitNor(x,y) |
~(x|y) using only ~ and
& |
1 | 8 |
bitXor(x,y) |
x^y using only ~ and
& |
2 | 14 |
bang(x) |
Compute !x without using ! |
4 | 12 |
The table above describes a set of functions that mimic existing functions in any modern processor. 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.
| Function | Description | Rating | Max Ops | |
|---|---|---|---|---|
copyLSB(x) |
set all bits of result to least significant bit of x | 2 | 5 | |
getByte(x,n) |
Extract byte n from word x | 2 | 6 | |
bitMask(highbit, lowbit) |
Generate a mask consisting of all 1's | 3 | 16 | |
bitCount(x) |
returns count of number of 1's in word | 4 | 40 |
The table above describes a set of functions that manipulate and
count the bits of an int variable. The
“rating” and “max ops” fields have the same
meaning as in Part I.
| Function | Description | Rating | Max Ops |
|---|---|---|---|
minusOne() |
return a value of -1 | 1 | 2 |
negate(x) |
return -x |
2 | 5 |
fitsBits(x,n) |
return 1 if x can be represented as an n-bit, two's complement integer. | 2 | 15 |
sm2tc(x) |
Convert from sign-magnitude to two's complement | 4 | 15 |
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.
| Function | Description | Rating | Max Ops |
|---|---|---|---|
isNotEqual(x,y) |
return 1 if x == y, and 0 otherwise |
2 | 5 |
isLess(x,y) |
if x < y then return 1, else return 0 |
3 | 24 |
isNonNegative(x) |
return 1 if x >= 0, return 0 otherwise |
3 | 6 |
isNonZero(x) |
Check whether x is nonzero using the legal operators except ! | 4 | 10 |
The table above describes a set of functions that implement standard comparisons between integers. The “rating” and “max ops” fields have the same meaning as in Part I.
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:
/u/cs252/bin/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 isNonZero
Before noon, Thursday, Jan. 24, submit your answers to the following 4 questions using Blackboard:
#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?
#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 0x00FF = %d.\n", *translation);
return 0;
}
|
bits.c
file?
btest print when compiled and run with the
original bits.c file?
The “trivia” assignment will be submitted via Blackboard.
The main assignment will be submitted using the script
/u/cs252/bin/TURNIN.
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
bits.c
bits.c (there is no separate README file for
this assignment)
For the “trivia” assignment: noon, Thursday, January 24.
For the main assignment: 11:59pm, Wednesday, January 30.