I'll get straight to the point: I'm freaking CLUELESS about Boolean Algebra, and I NEED to understand it. I have homework that I couldn't do many of the questions on due to my lack of understanding, and I have a test tomorrow in which I'm sure I'm going to need to fully understand it to pass.

I understand that there are the theorems (such as X * X = X, or that X * X' = 0, and the like, and I also understand things like DeMorgan's theorem and consensus theorem. But my issue is that I don't really know when to APPLY them. I can apply the consensus theorem, that's easy enough, but I don't see how to apply the other theorems because all the examples we've seen deal with single or double variable problems, while almost all of the problems on my homework are triple variable problems.

So I'll just post how far I got on one question, and maybe the help some of you can provide can give me a better understanding of what to do. I would be glad for any kind of help, because I seriously need it.

For the purposes of my post, X will be NOT X when I use an exclamation ( x2! ), and other variables will be shown as variations of X (X1, X2, X3, and so on). These problems are ALL in Sum of Products form, and must be simplified to the simplest possible form (they must, however, stay in Sum of Products form).

So for the first problem:
(X1 * X3) + (X1 * X2!) + (X1! * X2 * X3) + (X1! * X2! * X3!)

And I honestly have no clue where to go with that. I don't see a way to use consensus, and I don't really understand how to apply the other theorems to a three variable problem. I have the answer to this problem already, as it is in the back of the book, but of course they don't describe how they got to that point. Anyways, the answer is:
(X1 * X3) + (X2 * X3) + (X2! * X3!)

Essentially, I don't want your help with homework bullcrap (Although that would be nice), I seriously need to understand Boolean algebra so I can do it myself. Please, any help I can get would be fabulous. Thanks.

Alright guys, I THINK I got it down pretty well.

For example:
(X1! * X2! * X3) + (X1! * X2 * X3!) + (X1! * X2 *X3) + (X1 * X2! * X3!) + (X1 * X2 * X3!) + (X1 * X2! * X3) ->
X2! * X3 (X1! + X1) + X1 * X2 (X3 + X3!) + X1 * X3! (X2! + X2) using consensus
(X2! * X3) + (X1 * X2) + (X1 * X3!)

I see no where else it can go, and checking the final algorithm against the truth table (0 at only all 3 zeroes or all 3 ones) reveals that it does indeed work.

You know, I'd like to help, but I've never even heard of Boolean Algebra before. :laugh:

Where are the forums' math wizards?

I think I've got it down now. I had to use this theorem:
(x + x! * x2) = (x + x2)

Once I found that one out, I could finish most of them.


Yeah, where IS Dogsbody?