j.f.nault wrote

**Mine have 14 gates totals:**

-3 not gates

-8 and gates

-3 or gates

The one I found (4 gates total)

-1 not gate

-2 and gates

-1 or gates

So, now I’m confuse, Doest my success with the Mux gate was purely lucky, Do I misunderstood something about the canonical scenarios. I have the feeling that they are some way to optimise canonical representation to pass from 14 to 4 gate but I dont know how :S

And I don’t want to continue my read of the book til I don’t have a full understanding of this concept. So if someone could refer me to a (post/book/article etc.) that will be super appreciate :)

Thank a lot and sorry for my poor English and the super long text :)

You did very well learning to use the canonical representation to

**engineer **a solution for the Mux; it was not luck.

One of the better tools to use to simplify canonical representation is called a Karnaugh Map. Search the forum and you will find several references. This might be a

useful post.

You will also want to learn a bit about Boolean Algebra. It is like arithmetic algebra but for logic. The rules are similar, but not quite the same. A very powerful rule is called DeMorgan's law.

Another important observation that you made was the "key in the door". Another way to think about And gates is exactly that. Rename the inputs

*in* and

*key* and then the function of the And gate is

*in*->

*out* if

*key* is True and

*out*=False if

*key* is False.

--Mark