How Can CAD Software Simplify Complex 7-Variable Boolean Functions?

[electronic engineer]

Assume 7 variables like: C0,C1,C2,C3,C4,C5,C6

and the output function is : A=C6+C5'C4+C4'C3+C3'C2+C2'C1+C1'C0

well i know that the simplified function is:

A=C6+C5'C4+C3'C2+C1'C0

but i don't know why? and don't know how to simplify such 7-variables function using known algorithms (karnaugh,quinne-mccluskey...)
i think that it would be more comfortable to use CAD (computer aided design) rather than those algorithms in this case of more than 6 input variables...

anyway could anyone guide me through this problem and if I'm right about using CAD , i need to have a clue about it !

regards

 

[Manchot]

Well, C6 doesn't appear in any terms other than the one that it is in by itself, so you can ignore it initially and add it back in later. This leaves you with a six-variable equation, which is significantly easier to make a Karnaugh map out of.