K map and simplified circuit

Question

4) Draw the Karnaugh map and the resulting simplified circuit for the following function F(w, x, y, z) = !yz + w!y + !wzy + !w!xy!z + w!xy!z

    YZ
WX  00  01  11  10
00      1   1   1       
01      1   1
11  1   1   
10  1   1       1

Hi. The question above is given and I made that K-map (I think its right). The question I have is it asks for a resulting simplified circuit, I'm a little confused on what that means. Does it mean regroup the kmap and write out the wx + yz + whatever? Or do I draw question?

Since we are handing this in via .doc I'm assuming it is supposed to be regrouped but I'm not sure.

Sorry if this isnt the place to ask.

Answer 1

This isn't quite the place to ask these things, as mathematicians aren't that technological in general. Neither am I, but I assume the only thing you need to do here is to find the prime-implicants in this K-map and then you could use them to rewrite/simplify the given expression for F.

The prime-implicants for your example are: $\neg yz$, $w\neg y$, $\neg wz$ and $\neg xy\neg z$. The essential prime-implicants only contain $\neg xy\neg z$ and further, you just need to make sure you have covered all 1's. The simplification for $F(w,x,y,z) = \neg yz + w\neg y + \neg wzy + \neg w\neg xy\neg z + w\neg xy\neg z$ thus becomes $\tilde{F}(w,x,y,z) = \neg xy\neg z + \neg w z + w \neg z$

I hope this helps...