Computer Organization
Digital Logic Circuits(III)
Boolean Algebra ...

Solution Summary

This solution is comprised of a detailed explanation of the Three-Variable Exclusive-OR(Odd) Function.
It contains step-by-step explanation for the following problem:

It is an explanation for solving the problems of Boolean Algebra in Computer Organization.
Show that A(+)B(+)C = ABC +AB' C' + A'BC' + A'B'C , where (+) stands for the exclusive-OR microoperation,

that is, A exclusive-OR B exclusive-OR C = ABC +AB' C' + A'BC' + A'B'C
and verify your answer with truth table.

Which functions are one-to-one? Which functions are onto? Describe the inverse function
A)F:Z^2-N where f is f(x,y) x^2 +2y^2
B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd)
C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd)
D)h:N^3 -> N where h(x,y,z) = x + y -z

A fair dice is rolled. What is the probability of rolling an odd number OR a number less than 3?
Also would being able to speak Chinese and being able to speak Spanish be mutually exclusive events?

5. Determine fe(x) and fo(x). Is f even? Odd? Neither? - See attachment.
(g) x^4 + x^3 + x^2 + x + 1
(j) sin(sin x)
(k) cos(sin x)
(^ is raised to the power of)
fe(x) means even function.
fo(x) means odd function.

1a.)Is y=x^4 a single- or multi-valued function?
b.)Is y=f(x)=x^2+4x an even, odd, or neither
function?
c.)What is the inverse function of y=x^4
d.)What is the inverse function of (b.),y=x^2+4x?
e.)Is the inverse function from (d.), odd, even, or
neither?

An even function is defined as f(x) = f(-x), and an odd function has -f(x) = f(-x).
The domain of a function is the set of input data that keeps the function defined.
Determine if the function f(x) = -2x^2 * absolute value(-6x) is even, odd, or neither.
Find the average rate of change for the function f(x) = 4/(x+3) between t

A function is defined as followed:
see attachment
Where f(t+2)=f(t) that is, f(t) has period 2.
i) Draw a plot of the function f(t). Comment fully on whether the function is even or odd or none of these.
ii) Find the first four non-zero coefficients for the Fourier series expansion of the function f(t)
iii) Using eg. e

Signal Processing & Wavelength. Problems # 6-7. See attached file for full problem description.
6. For each of the signals given, determine mathematically if the signal is even, odd, or neither. Sketch the waveforms to verify your results. For signals that are neither, find the even or odd parts of the signal.
a) x(t) = 5u(t