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# Assignment 1: Data Representation and Computer Arithmetic

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Programming Assignment 1: Data Representation and Computer Arithmetic
1 Introduction
This assignment is designed to help you learn the representation, interpretation, and manipulation of data in its internal representation. There are two parts. In the ﬁrst part, you will implement a program calc to add and subtract numbers speciﬁed in diﬀerent bases (multiplication is extra credit). In the second part, you will implement a program format that will print the decimal values of bit sequences representing integer and ﬂoating point data types.
2 Numeric Base Conversion and Calculator
Implement a program called calc with the following usage interface:
calc <op <number1 <number2 <output base
The ﬁrst argument, <op, is either the string “+”, for addition, or “-”, for subtraction. If you want to implement multiplication, then <op can also be the string “*”. (If you do implement multiplication, make sure to say so in your readme.pdf ﬁle so that the TAs know to check your program for this functionality.) The next two arguments, <number1 and <number2 are 64-bit, two’s-complement integers. Each of these numbers will be given in the form of:
?(b|o|d|x)dndn−1…d1d0
which can be interpreted as: a base indicator where b means that the number is a binary number, o means octal, x means hexadecimal and d means decimal. dndn−1…d1d0 are the digits of the number. A decimal number may be preceded by a minus sign. Note that a minus sign is neither meaningful nor necessary for binary, octal or hexadecimal numbers as the bit pattern for these representations already covers positive and negative quantities. The ﬁnal argument, <output base, gives the base for the resulting output number. Like the base indicator for the input numbers, this argument can be one of four strings: “b” for binary, “o” for octal, “d” for decimal, and “x” for hexadecimal. Your program should output the answer in the same form as the input numbers (that is, the output number should follow the regular expression given above). Some examples:
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\$ ./calc + d1111111111111111 d1111111111111111 d d2222222222222222 \$ ./calc + b1101 b1 d d14 \$ ./calc + d999999999 d1 d d1000000000 \$ ./calc – d10 -d4 b b1110 \$ ./calc + -d10 -d4 b b11111111111111111111111111110010
Given that 64-bit binary numbers can only handle numbers within a ﬁnite size and range, your program must therefore check to make sure that any input given to it will ﬁt into a 64-bit integer. Any input that does not ﬁt into a 64-bit integer should be ﬂagged as an error. Important: You must write the base conversion code yourself. You may not use type-casting, libraries, or output formats in printf(). You may use standard C arithmetic operations. You may use the C standard libraries for functionality not related to the conversion (e.g., string handling functions). Important: If calc detects an error in the inputs, it should print out an error message that starts with the string “ERROR”, followed by a string that gives an informative message about the error that it detected.
3 Format Interpretation
Implement a program called format with the following usage interface:
format <input bit sequence <type
The ﬁrst argument, <input bit sequence, is a sequence of 64 bits. Remember that your C program will get it as a string of 1 and 0 characters in the argv[1] argument to main. This sequence of bits represents the binary values stored in 4 contiguous bytes in memory. The leftmost bits are stored in the byte with the smallest address while the rightmost bits are stored in the byte with the largest address. The second argument, <type, gives the type that you should use to interpret the input bit sequence, and can be either int (integer) or float. The formats for the input bit sequence is as follows. If the type is:
int: the format is two’s complement;
float: the format is IEEE 754 single precision;
Note that the input bit sequence can correspond to negative numbers. Your program should print out the decimal representation of the input bit sequence, assuming a big endian byte ordering. Floating point numbers should be printed in scientiﬁc notation, where a
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number 1.5×105 would be printed as 1.5e5. For positive inﬁnity, output pinf, for negative inﬁnity, output ninf, and for “NaN”, output NaN. Here are some examples:
\$ ./format 01000001010000100100001101000100 int 1094861636
\$ ./format 10000001010000100100001101000100 int -2126363836
\$ ./format 01000001010000100100001110000100 int 1094861700
\$ ./format 00000000000000000000000000000001 int 1
\$ ./format 01000000110000110100001111010100 float 6.10203e0
\$ ./format 00111010000111111111011000001000 float 6.102030e-4
\$ ./format 10000000000000000000000000000000 float -0.0e0
\$ ./format 01000000010010010000111111011011 float 3.141593e0
Important: You must write the interpretation code yourself. You may not use type-casting, libraries, or output formats in printf(). You may use standard C arithmetic operations. You may use the C standard libraries for functionality not related to the value interpretation (e.g., string handling functions). Important: If format detects an error in the inputs, it should print out an error message that starts with the string “ERROR”, followed by a string that gives an informative message about the error that it detected. For this program, you can assume that any input bit sequence that is shorter or longer than 32 bits is erroneous.
4 Submission
You have to e-submit the assignment using Sakai. Your submission should be a tar ﬁle named pa1.tar that can be extracted using the command:
tar xvf pa1.tar
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• readme.pdf: this ﬁle should describe your design and implementation of the calc program. In particular, it should detail your design, any design/implementation challenges that you ran into, and an analysis (e.g., big-O analysis) of the space and time performance of your program. • makefile: there should be at least the following rules in your makefile: all build both your calc and format executables. calc build your calc executable. format build your format executable. clean remove all object ﬁles and executables. Prepare for rebuilding from scratch.
• source code: All source code and header ﬁles necessary for building your calc and format executables. These should at least include calc.c and format.c.
You can build your pa1.tar ﬁle in the following steps: 1. Put all the ﬁles you want to hand in in a subdirectory called pa1. 2. In the parent directory that contains pa1, invoke tar:
tar cvf pa1.tar pa1
The arguments to tar are cvf. The c tells tar to create a new archive ﬁle. The f tells tar that the next command line argument is the name of the output ﬁle. The v just makes tar list the ﬁles it’s putting into the archive. We will compile and test your program on the iLab machines so you should make sure that your code can be extracted from your pa1.tar ﬁle on the iLab machines and that your program compiles and runs correctly on these machines. You must compile all C code using the gcc compiler with the -Wall ﬂags.
5.1 Functionality
This is a large class so that necessarily the most signiﬁcant part of your grade will be based on programmatic checking of your program. That is, we will build a binary using the Makeﬁle and source code that you submitted, and then test the binary for correct functionality against a set of inputs. Thus:
• You should make sure that we can build your program by just running make. • You should test your code as thoroughly as you can. In particular, your code should be adept at handling exceptional cases.
Be careful to follow all instructions. If something doesn’t seem right, ask.
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5.2 Design
Having said the above about functionality, design is a critical part of any programming exercise. In particular, we expect you to write reasonably eﬃcient code based on reasonably performing algorithms and data structures. More importantly, you need to understand the performance (time & space) implications of the algorithms and data structures you chose to use. Thus, the explanation of your design and analyses in the readme.pdf will comprise a non-trivial part of your grade. Give careful thoughts to your writing of this ﬁle, rather than writing whatever comes to your mind in the last few minutes before the assignment is due.
5.3 Coding Style
Finally, it is important that you write “good” code. Unfortunately, we won’t be able to look at your code as closely as we would like to give you good feedback. Nevertheless, a part of your grade will depend on the quality of your code. Here are some guidelines for what we consider to be good:
• Your code is modularized. That is, your code is split into pieces that make sense, where the pieces are neither too small nor too big. • Your code is well documented with comments. This does not mean that you should comment every line of code. Common practice is to document each function (the parameters it takes as input, the results produced, any side-eﬀects, and the function’s functionality) and add comments in the code where it will help another programmer ﬁgure out what is going on. • You use variable names that have some meaning (rather than cryptic names like i).
Further, you should observe the following protocols to make it easier for us to look at your code:
• Deﬁne prototypes for all functions. • Place all prototype, typedef, and struct deﬁnitions in header (.h) ﬁles. • Error and warning messages should be printed to stderr using fprintf().
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Assignment 1: Data Representation and Computer Arithmetic
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