COMP201 - Assignment 1 - Data Lab - Manipulating Bits - Solved

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.



There are a number of files 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 15 programming puzzles. Your assignment is to complete each function skeleton using only straightline code for the integer puzzles (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:

! ˜ & ˆ | + << >>

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
isZero(x)
Is x == 0?
1
2
implication(x,y)
x -> y in propositional logic[1]
2
5
twoDigitNumberInBaseFour(x,y)[2]
Integer equivalent of (xy)4
2
4
multThreeEighths(x)
Multiply x by 3/8 rounding toward 0
3
12
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
tmax()
Most positive two’s complement integer
1
4
isOppositeSigns(x,y)
Do x and y have different signs?
3
6
conditional(x,y,z)
Same as x ? y : z
3
16
Table 2: Two’s Complement Arithmetic Functions

4.3      Floating-Point Operations

For this part of the assignment, you will implement some common single-precision floating-point operations. 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 constants. Instead, any floating-point operand will be passed to the function as having type unsigned, and any returned floating-point value will be of type unsigned. Your code should perform the bit manipulations that implement the specified floating point operations.

Table 3 describes a set of functions that operate on the bit-level representations of floating-point numbers. Refer to the comments in bits.c and the reference versions in tests.c for more information.

Name
Description
Rating
Max Ops
float_abs(uf)
Compute |f|
2
10
float_f2i(uf)
Compute (int) f
4
30
Table 3: Floating-Point Functions. Value f is the floating-point number having the same bit representation as the unsigned integer uf.

Functions float_abs and float_f2i must handle the full range of possible argument values, including not-a-number (NaN) and infinity. The IEEE standard does not specify precisely how to handle NaN’s, and the IA32 behavior is a bit obscure. We will follow a convention that for any function returning a NaN value, it will return the one with bit representation 0x7FC00000.

The included program fshow helps you understand the structure of floating point numbers. To compile fshow, switch to the handout directory and type:

$ make

You can use fshow to see what an arbitrary pattern represents as a floating-point number:

$ ./fshow 2080374784

Floating point value 2.658455992e+36

Bit Representation 0x7c000000, sign = 0, exponent = f8, fraction = 000000 Normalized. 1.0000000000 X 2ˆ(121)

You can also give fshow hexadecimal and floating point values, and it will decipher their bit structure.


•   btest: This program checks the functional correctness of the functions 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’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 isZero

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

$ ./btest -f isOppositeSigns -1 7 -2 10

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:

$ ./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.

•   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:

$ ./driver.pl


6          Handin Instructions
I         Write your name and student number in bits.c file - line 4 as comment.

II       Commit all the changes you make: $ git commit -a -m "final commit"

III     Push your work to GitHub servers: $ git push origin master

7          Advice
•   Don’t 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.

•   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 */

}

•   Use linuxpool.ku.edu.tr linux servers to test your code in order to avoid compatibility issues.

8          How to use linuxpool.ku.edu.tr linux servers
I         Connect to KU VPN (If you are connected to the KU network, you can skip this step.)

See for details: https://confluence.ku.edu.tr/kuhelp/ithelp/it-services/network-and-wireless/vpn-access

)

III     When you are finished with your work, you can disconnect by typing: $ exit

Your connection to the server may drop sometimes. In that case, you need to reconnect.

We advice you to watch the following video about the usage of SSH, which is used to connect remote servers, and SCP, which is used to transfer files between remote servers and your local machine:

https://www.youtube.com/watch?v=rm6pewTcSro

 
 How to connect and disconnect using SSH

 
[1] See the following web page for the truth tables: http://sites.millersville.edu/bikenaga/math-proof/truth-tables/truth-tables.html
[2] For twoDigitNumberInBaseFour(x,y), you can assume x,y ∈{0,1,2,3}