Operands : AND and XOR

What is the value of x after each of the following statements are encountered in a computer program, if x = 1 before the statement is reached. Explain fully. (a) if 2 + 3 = 6 AND 3 + 4 = 7 then x:= x + 1 (b) if 2 + 3 = 6 XOR 3 + 4 = 7 then x:= x + 1

Rule of Products

A bit string is a string of bits (0’s and 1’s). The length of a bit string is the number of bits in the string. An example, of a bit string of length four is 0010. An example, of a bit string of length five is 11010. Use the Rule of Products to determine the following: (a) How many bit strings are there of length eight? Explain. (b) How many bit strings are there of length eight which begin with two 1’s? Explain.

Matrix Addition and Multiplication and Applying the Distributive Law

Compute: (a) AC + BC (It is much faster if you use the distributive law for matrices first.) (b) 2A - 3A See attached file for full problem description.

Basic Matrix Laws

Let A and B be arbitrary n x n matrices whose entries are real numbers. Use basic matrix laws only to expand (A + B)². Explain all steps. Hint: Use the distributive laws.

One to One and Inverse Functions

Let A = {1,2,3} and B = {a,b,c}, and let f: A B. (a) Give an example of a one to one function from A to B (use the given sets A and B above). Briefly explain why your example is a 1-1 (one-to-one) function. (b) How many one to one functions from A to B are there? Explain. (c) Using the above sets A and B define a function f-1, for some function f from A to B. (d) Is the function g: R R defined by g(n) = a one to one function? (Be careful, means the ceiling function.) Explain. See attached file for full problem description.