# Lab 1: Manipulating Bits Using C

Assigned Wednesday, March 28, 2012 Friday, April 6, 2012 at 5:00p lab1.tar.gz

## Overview

The purpose of this assignment is to become more familiar with data at the bit-level representation. You'll do this by solving a series of programming "puzzles". Many of these puzzles are quite artificial, but you'll find yourself much more about bit representations in working your way through them.

## Instructions

The lab1 folder contains a number of tools, described later, and a bits.c file. bits.c contains a skeleton for each of the programming puzzles, along with a large comment block that describes exactly what the function must do and what restrictions there are on its implementation. Your assignment is to complete each function skeleton using:

• only straightline code (i.e., no loops or conditionals);
• a limited number of C arithmetic and logical operators; and
• no constants longer than 8 bits.

The intent of the restrictions is to require you to think about the data as bits - because of the restrictions, your solutions won't be the most efficient way to accomplish the function's goal, but the process of working out the solution should make the notion of data as bits completely clear.

## The Puzzles

This section describes the puzzles that you will be solving in bits.c. More complete (and definitive, should there be any inconsistencies) documentation is found in the bits.c file itself.

### Bit Manipulations

The table below describes a set of functions that manipulate and test sets of bits. The Rating column gives the difficulty rating (the number of points) for each puzzle and the Description column states the desired output for each puzzle along with the constraints. 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.

Rating Function Name Description
1 bitAnd x & y using only ~ and |
1 bitOr x | y using only ~ and &
1 isZero returns 1 if x == 0, else 0
2 getByte extract byte n from word x
3 isGreater return 1 if x > y, else 0
3 replaceByte replace byte n in x with c
3 rotateLeft rotate x to the left by n
4 bitCount returns the number of 1's in word
4 isNonZero returns 0 if x == 0, else 1

### Two's Complement Arithmetic

The following table 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.

Rating Function Name Description
1 isTmax returns 1 if x is the maximum 2's complement number, else 0
2 isNegative return 1 if x < 0, else 0
2 fitsBits returns 1 if x can be represented as an n-bit, two's complement integer
3 addOK whether you can compute x + y without overflow

## Checking Your Work

We have included two tools to help you check the correctness of your work.

`dlc` 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:

``\$ ./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:

``\$ ./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.

`btest` is a program that checks the functional correctness of the code in bits.c. To build and use it, type the following two commands:

``````\$ make
\$ ./btest``````

Notice that you must rebuild `btest` each time you modify your bits.c file. (You rebuild it by typing `make`.) 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:

``\$ ./btest -f bitNor``

You can feed it specific function arguments using the option flags `-1`, `-2`, and `-3`:

``\$ ./btest -f bitNor -1 7 -2 0xf``

Check the file README for documentation on running the `btest` program.

Do not include the `<stdio.h>` 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 `<stdio.h>` header, although `gcc` will print a warning that you can ignore.

You should be able to use the debugger on your code. For example:

``````\$ make
gcc -O -Wall -m32 -g -lm -o btest bits.c btest.c decl.c tests.c
gcc -O -Wall -m32 -g -o fshow fshow.c
gcc -O -Wall -m32 -g -o ishow ishow.c
\$ gdb ./btest
GNU gdb (GDB) Fedora (7.1-34.fc13)
Copyright (C) 2010 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.  Type "show copying"
and "show warranty" for details.
This GDB was configured as "i686-redhat-linux-gnu".
For bug reporting instructions, please see:
<http://www.gnu.org/software/gdb/bugs/>.
Reading symbols from /homes/iws/dvhc/cse351/lab1/src/btest...done.
(gdb) b bitNor
Breakpoint 1 at 0x8048717: file bits.c, line 144.
(gdb) r
Starting program: /homes/iws/dvhc/cse351/lab1/src/btest
ScoreRatingErrorsFunction

Breakpoint 1, bitNor (x=-2147483648, y=-2147483648) at bits.c:144
144}
(gdb) p x
\$1 = -2147483648
(gdb) p/x x
\$2 = 0x80000000
(gdb) q
A debugging session is active.

Inferior 1 [process 12728] will be killed.

Quit anyway? (y or n) y``````

The `dlc` program enforces a stricter form of C declarations than is the case for C++ or that is enforced by `gcc`. In particular, in a block (what you enclose in curly braces) all your variable declarations must appear before any statement that is not a declaration. For example, `dlc` 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 */
}``````

Instead, you must declare all your variables first, like this:

``````int foo(int x)
{
int a = x;
int b;
a *= 3;
b = a;
}``````

## Submitting Your Work

Please submit your completed bits.c file through the Catalyst Drop Box for this assignment.