I'm taking Computer Architecture and we were given a list of simple Boolean Rules. I'm having trouble finding out where to start.
This is my work so far
F = y'z' + xy'z + xz' + x'yz'
F = y'((1)z'+x(1)z)+z'(x+x'y(1))
F = y'(z'+xz)+z'(x+x'y)
F = y'(xz'+zz')+z'(xx'+xy)
F = y'(xz'+0)+z'(0+xy)
F= y'(xz')+z'(xy)
F= y'(xz')+z'(xy(1))
F= y'(xz')+z'(xy(x+x'))
At this point I feel like I have too many terms.
As a general approach, you should see which variable or negation thereof the terms have in common. In fact, see which one(s) is being shared the most. In this case, I see $3$ terms that include $z'$, so I would start with that:
$ y'z' + xy'z + xz' + x'yz' =$
$ z'(y'+ x + x'y) + xy'z$
Now let's see what we can do with the $y'+x+x'y$ term:
Well, as a very useful principle we have:
Reduction
$p+p'q=p+q$ (in the context of $p$, the $p'q$ term reduces to just $q$
If Reduction is not on your list, too bad, since it is really super handy. We can derive it from more basic principles, which is why it is not always given to you:
$p+p'q=(p+p')(p+q)=(1)(p+q)=p+q$
Applying Reduction:
$y'+x+x'y=y'+y=1$
Ah, super! So this means that your function can be simplified to:
$z'(y'+x+x'y)+xy'z=z'(1)+xy'z=z'+xy'z$
And now we can do one more application of Reduction to get:
$z'+xy'$