Project Grade: 100.0/100.0

Completed Spring of 2022 as a part of Lehigh University's CSE 202: Computer Organization and Architecture.

Note:

All programs were written and optimized for X86-64 machines with gcc module 7.10.

CSE202-Big-Integer-SP2022

Big-Integer: A programming exercise to create a new type for big integers (128 bits), store, access and manipulate big integers using bit-level and arithmetic operations

Learning Objectives

1. Create a programmer-defined data type for big integers represented on 128 bits using C structures

2. Define a function to read a string from the standard input and store it in memory as two quadruple words (128 bits) using C unions for the little endian order

3. Define six functions for bitwise operations to manipulate big integers as two quadruple words (not, and, or, xor, shift left, and shift right)

4. Define a function to add two big integers on 128 bits using the integer addition on 64 bits

5. Define a function to output the binary representation of a big integer from memory to the standard output using unions

Instructions

Write a C program named big_integer.c to accept two or three command-line arguments as listed below:

1. An operation from the set {"not", "and", "or", "xor", "sl", "sr", "add"}
2. 32 hex characters (most significant on the left) for the first operand of the operation, or
3. An unsigned integer for the number of positions for the shift operations only
4. Another 32 hex characters for the second operand of the binary operations only The 32 hex characters (one or two depending on the operation) should be stored in 16 adjacent bytes in memory that represent the big integer type (128 bits) using a union.

Here are examples of the program runs:

1. "not" operation $> ./prog0 not ffffffffffffffffffffffffffffffff

~ ffffffffffffffffffffffffffffffff = 00000000000000000000000000000000

2. shift left operation $> ./prog0 sl 25 ffffffffffffffffffffffffffffffff

ffffffffffffffffffffffffffffffff << 25 = fffffffffffffffffffffffffe000000

3. shift right operation $> ./prog0 sr 12 ffffffffffffffffffffffffffff000

fffffffffffffffffffffffffffff000 >> 12 = ffffffffffffffffffffffffffffffff

4. and operation $> ./prog0 and ffffffffffffffffffffffffffffffff 0000ffffffffffffffffffff00000000

ffffffffffffffffffffffffffffffff & 0000ffffffffffffffffffff00000000 = 0000ffffffffffffffffffff00000000

5. or operation $> ./prog0 or ffffffffffffffffffffffffffffffff 0000ffffffffffffffffffff00000000

ffffffffffffffffffffffffffffffff | 0000ffffffffffffffffffff00000000 = ffffffffffffffffffffffffffffffff

6. xor operation $> ./prog0 xor ffffffffffffffffffffffffffffffff 0000ffffffffffffffffffff00000000

ffffffffffffffffffffffffffffffff ^ 0000ffffffffffffffffffff00000000 = ffff00000000000000000000ffffffff

7. add operation $> ./prog0 add ffffffffffffffffffffffffffffffff 0000ffffffffffffffffffff00000000

ffffffffffffffffffffffffffffffff + 0000ffffffffffffffffffff00000000 = 0000fffffffffffffffffffeffffffff

8. Input error (invalid operand, not hexadecimal) $> ./prog0 not ffff111122223333444455556666777g

Invalid input 'ffff111122223333444455556666777g' Usage: ./prog0 op [k] number1 [number2] op: operation from {not, sl, sr, and, or, xor, add} k: shift positions for operations 'sl' and 'sr' number1: operand in hex for unary operations 'not', 'sl', 'sr' or first operand in hex for binary operations 'and', 'or', 'xor', 'add' number2: second operand in hex for binary operations only

9. Input error (invalid operation) $> ./prog0 sub ffffffffffffffffffffffffffffffff 0000ffffffffffffffffffff00000000

Invalid operation 'sub' Usage: ./prog0 op [k] number1 [number2] op: operation from {not, sl, sr, and, or, xor, add} k: shift positions for operations 'sl' and 'sr' number1: operand in hex for unary operations 'not', 'sl', 'sr' or first operand in hex for binary operations 'and', 'or', 'xor', 'add' number2: second operand in hex for binary operations only

Approach

1. After verifying the input is valid, read the input 32 hex characters into the union's 16 character array. Do not forget to consider "Little Endian" for the system you are compiling and running on. You want to be able to access those same 16 bytes of the character array as a big integer (two quadwords).

2. After storing the hex digits, you will perform the operation and store the result in a big integer type variable.

3. Print the operation, its operands, and the result as shown in the examples above.