CS 281, Fall 2019
Data Lab: Manipulating Bits
Assigned: Sept. 16, Due: Mon., Sept. 30, 11:59PM
1 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.
2 Logistics
This is an individual project. All handins are electronic. Clarifications and corrections will be posted on the
course Web page.
3 Handout Instructions
On Notebowl, there is an assignment entitled “Datalab” where you can find a repository named datalab-
handout.tar. Download this file to your account in the Linux Lab or your personal computer.
Start by copying datalab-handout.tar to a (protected) directory on a Linux machine in which you
plan to do your work. 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 12 programming puzzles. Your assignment is to
complete each function skeleton using only straightline code for the integer puzzles (i.e., no loops or con-
ditionals) and a limited number of C arithmetic and logical operators. Specifically, you are only allowed to
use the following eight operators:
! ˜ & ˆ | + << >>
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A few of the functions further restrict this list. Also, you are not allowed to use any constants longer than 8
bits. See the comments in bits.c for detailed rules and a discussion of the desired coding style.
4 The Puzzles
This section describes the puzzles that you will be solving in bits.c.
4.1 Bit Manipulations
Table 1 describes a set of functions that manipulate and test sets of bits. The “Rating” field gives the
difficulty rating (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. See the comments in bits.c for more
details on the desired behavior of the functions. You may also refer to the test functions in tests.c. These
are used as reference functions to express the correct behavior of your functions, although they don’t satisfy
the coding rules for your functions.
Name Description Rating Max Ops
bitAnd(x,y) x & y using only | and ˜ 1 8
getByte(x,n) Get byte n from x. 2 6
logicalShift(x,n) Shift right logical. 3 20
bitParity(x) returns 1 if x contains an odd number of 0’s. 4 20
bang(x) Compute !n without using ! operator. 4 12
Table 1: Bit-Level Manipulation Functions.
4.2 Two’s Complement Arithmetic
Table 2 describes a set of functions that make use of the two’s complement representation of integers. Again,
refer to the comments in bits.c and the reference versions in tests.c for more information.
Name Description Rating Max Ops
tmin() Most negative two’s complement integer 1 4
fitsBits(x,n) Does x fit in n bits? 2 15
divpwr2(x,n) Compute x/2n 2 15
negate(x) -x without negation 2 5
isPositive(x) x > 0? 3 8
isLessOrEqual(x,y) x <= y? 3 24
conditional(x) same as x ? y : z 3 16
Table 2: Arithmetic Functions
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5 Evaluation
Your score will be computed out of a maximum of 60 points based on the following distribution:
30 Correctness points.
24 Performance points.
6 Style points.
Correctness points. The 12 puzzles you must solve have been given a difficulty rating between 1 and 4, such
that their weighted sum totals to 41. 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.
Style points. Finally, we’ve reserved 6 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.
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.
• 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 bitAnd
You can feed it specific function arguments using the option flags -1, -2, and -3:
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unix> ./btest -f bitAnd -1 7 -2 0xf
Check the file README for documentation on running the btest program.
• dlc: This is a modified version of an ANSI C compiler from the MIT CILK group 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 non-straightline 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
Your instructors will use driver.pl to evaluate your solution.
6 Handin Instructions
Submit your bits.c file to the “Datalab” assignment on the course Notebowl page. The timestamp on the
submission determines the time the project was completed (subject to a 10% lateness penalty per 24 hours
late).
7 Advice
• Don’t include the header file in your bits.c file, as it confuses dlc and results in
some non-intuitive error messages. You will still be able to use printf in your bits.c file for
debugging without including the header, although gcc will print a warning that you
can ignore.
• The dlc program 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 */
}
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8 The “Beat the Prof” Contest
For fun, we’re offering an optional “Beat the Prof” contest that allows you to compete with other students
and the instructor to develop the most efficient puzzles. The goal is to solve each Data Lab puzzle using the
fewest number of operators. Students who match or beat the instructor’s operator count for each puzzle are
winners!
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://imbueai.duckdns.org:8080
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