EECS 213
Lab L1: Manipulating Bits

Due: Monday, October 3, 11:59PM

Introduction

The purpose of this assignment is to become more familiar with bit-level representations and manipulations. You'll do this by solving a series of programming "puzzles." Many of these puzzles are quite artificial, but working on them should help increase your understanding of low-level data representations.

You may work alone or with a partner on this lab. The only "hand-in" will be electronic. Any clarifications and revisions to the assignment will be posted on the course help system.

You'll need a real Linux system for this lab; Cygwin won't run the dlc binary described below. Contact me if you need a TLAB account.

Setup Instructions

Copy datalab-handout.tar to the directory in which you plan to do your work, e.g., eecs213/datalab.

Extract the files you need with the command tar xvf datalab-handout.tar.

There are two programs that you use to check your code for this assignment. dlc is a compiler binary that you can use to check your solutions for compliance with the coding rules. Make sure that ./dlc runs without error.

The other tester is btest. Use the command make btest to build btest with the current version of bits.c. If btest builds without error, then run it with ./btest -g. If you do this right now, you'll see that bits.c fails all tests. Your goal is to fix bits.c to get rid of those failures.

The file README contains additional documentation you need to know about btest.

The bits.c file contains a skeleton for 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 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. See the comments in bits.c for detailed rules and a discussion of the desired coding style.

Evaluation

Your code will be compiled with gcc and tested on my machine. Your score will be computed out of a maximum of 75 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 40. 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 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 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.

Beat the Prof!

To see how good your current solution is, you can submit it and see how it compares to a good (but not absolute best) "professor" solution. Simply run the command ./driver.pl -u name. This runs a Perl script that runs dlc and btest and sends the data to a web server. For name, use something distinctive, like your first names, e.g., ./driver.pl -u PatAndSandy.

To see the current results, check

The DataLab Scoreboard.

Note: it might take a minute or so to show up. Be sure to refresh the page. If nothing changes in a short time, email the professor.

Submitting to Beat the Prof is not the same as handing in the final version.

Part I: Bit manipulations

This table 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.

Function bitNor computes the nor (not-or) function. When applied to arguments x and y, it returns ~(x|y). You may only use the operators & and ~. Function bitXor should duplicate the behavior of the bit operation ^, using only the operations & and ~.

Function isNotEqual compares x to y for inequality. As with all predicate operations, it should return 1 if the tested condition holds and 0 otherwise.

Function getByte extracts a byte from a word. The bytes within a word are ordered from 0 (least significant) to 3 (most significant). Function copyLSB replicates a copy of the least significant bit in all 32 bits of the result. Function logicalShift performs logical right shifts. You may assume the shift amount n satisfies 1 ≤ n ≤ 31.

Function bitCount returns a count of the number of 1's in the argument. Function bang computes logical negation without using the ! operator. Function leastBitPos generates a mask consisting of a single bit marking the position of the least significant one bit in the argument. If the argument equals 0, it returns 0.

Part II: Two's Complement Arithmetic

This table describes a set of functions that make use of the two's complement representation of integers.

Function tmax returns the largest integer.

Function isNonNegative determines whether x is less than or equal to 0.

Function isGreater determines whether x is greater than y.

Function divpwr2 divides its first argument by 2ⁿ, where n is the second argument. You may assume that 0 ≤ n ≤ 30. It must round toward zero.

Function abs is equivalent to the expression x<0?-x:x, giving the absolute value of x for all values other than TMin.

Function addOK determines whether its two arguments can be added together without overflow.

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 gcc. 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. The typical usage is

./dlc bits.c

Type ./dlc -help for a list of command line options. The README file is also helpful. Some notes on dlc:

• The dlc program runs silently unless it detects a problem.
• Don't include <stdio.h> in your bits.c file, as it confuses dlc and results in some non-intuitive error messages.

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 isPositive.

Hand In Instructions

Submitting solutions to Beat the Prof is not the same as handing in your final answer. To hand in your solution:

• Make sure you and your partner, if any, are identified in bits.c.
• Remove any extraneous print statements from bits.c
• Email just bits.c to c-riesbeck@northwestern.edu with the Subject line: EECS 213 Datalab