1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Disjunctive Normal form to Combinatorial Circuit

  1. Apr 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Draw the combinatorial circuit corresponding to the disjunctive normal form.
    2.PNG
    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. jcsd
  3. Apr 13, 2016 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
  4. Apr 13, 2016 #3
    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?
     
  5. Apr 14, 2016 #4

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No. In fact the expression cannot be factorized at all.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Disjunctive Normal form to Combinatorial Circuit
  1. Combinatory problem. (Replies: 17)

  2. Combinatorial Identity (Replies: 2)

Loading...