Programming Assignments/Solutions to Discrete Structures for Computing Applications II Fall 2020

1. Given two integers, use the Euclidean algorithm to find their greatest common divisor.

2. Convert Binary String to Decimal

3. Design a class named Rectangle to represent a rectangle. The class contains: • Two double data fields named width and height that specify the width and height of the rectangle. • A no-arg constructor that creates a rectangle with width 1 and height 1. • A constructor that creates a rectangle with the specified width and height. • A function named getArea()that returns the area of this rectangle. • A function named getPerimeter() that returns the perimeter. Implement the class. Write a test program that creates two Rectangle objects. Assign width 4 and height 40 to the first object and width 3.5 and height 35.9 to the second. Display the width, height, area, and perimeters of the first object and then the second object

4. Generate valid keys (e,n) for the RSA cryptosystem.

5. Use the Sieve of Eratosthenes to find all primes less than 10,000(or in this case the user can choose).

6. Find all of the positive divisors of a positive integer from its prime factorization.