# Disjunctive Normal form to Combinatorial Circuit

1. Apr 13, 2016

### Kingyou123

1. The problem statement, all variables and given/known data
Draw the combinatorial circuit corresponding to the disjunctive normal form.

2. Relevant equations
DNF of f(x,y,z)=xyz+Not(xy)z
3. The attempt at a solution
f(x,y,z)=xyz+not(xy)z
=z(xy+not(xy))
Wouldn't the xy and not xy cancel out? That's my current problem with this probelm.

2. Apr 13, 2016

### andrewkirk

The problem is that your DNF is not correct. Presumably the first term is supposed to give the 1 in the second row of the last column. But z is 0 in that row. So why are none of x,y,z negated in the term?
Your second term is not correct either. Are you aware that not(xy) is not the same as not(x)not(y)? de Morgan's Laws can sort that out for you.

3. Apr 13, 2016

### Kingyou123

Oh thank you for catching my mistake, I was looking at row 0 for some reason.
So I'm left with xynot(z) + not(x)not(y)z, wouldn't everything just cancel out?

4. Apr 14, 2016

### andrewkirk

No. In fact the expression cannot be factorized at all.