Computing the number of intergers that can be represented using sign or two's complement.

Using a 32-bit word, how many different integers can be represented by (a) sign and modulus; (b) 2's complement? Express the answer using powers of 2.

Determining the bias, largest and smallest floating point number and machine precision in IEEE single precision system.

Suppose in IEEE single precision, the width of the exponent field is 3, not 8, and the width of the fraction field is 5, not 23. (a) What should the exponent bias be? (b) What are the largest and smallest nonnegative normalized floating point numbers in this system? (c) What is the machine epsilon of this system?

Solving linear systems using Gaussian Elimination with Partial Pivoting.

Solve the following system using Gaussian elimination with partial pivoting: |1 −1 2 |---- |x1|-----|-2 | |−2 1 −1 |--- |x2|--=-| 2 | |4 −1 2 |-----|x3|----|-1 | Show intermediate matrices, vectors and multipliers at each step.

Writing a program to calculate pythagorean triples.

A right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the hypotenuse. Write a program to find all Pythagorean triples for side1, side2 and the hypotenuse. All must be no larger then 500. Use a triple-nested for/next loop that tries all possibilities.

Maclaurin Series program in VBA/Excel

Write a VBA program to evaluate this series for x = .512. Continue your series until a term less than 10-8 is computed. See attachment