boolean algebra simplyfing

Question

I need to solve these expressions with boolean algebra:

$$Z = a'bc+ab'c+abc'+abc\mbox{ AND }Z = a'(b+db'c')+a'b'(d'c'+c)$$

Every advice is more then welcome. Thanks

Answer 1

One way of doing it would be to expand both expressions to their respective CDNFs (with respect to $a,b,c$ and $d$), and see if any of the canonical conjunctions overlap. In your case, these two canonical conjunctions are part of both CDNFs: $a'bcd'$ and $a'bcd$.

So, the solution is: $a'bcd' \vee a'bcd = a'bc$.