Math Is Fun Forum

How?

The circuit has 6 gates, 4 without the NOTs. 

When I partly did the question, I had 4 of the gates done for you.

How have you got it to just 3 gates?

What happened after  ( (p' OR ...) OR (...AND...) )

Bob

fourth is eulerian too

hi dee93

It cannot be the same as the other question because the logic statements are different.

Let's go back to first principles. 

pq' means p is true and not q is true (or q is false)

A karnaugh map is a way of showing a logic expression diagrammatically.  It does a similar job to the venn diagrams I did earlier but copes better when the number of variables goes up.

In the boxes you can put expressions like pq'r or use 0 for false an d 1 for true (101 for this case) or express the logic in words: p true, q false, r true.  Below I've taken the earlier diagram and added more labels to show what each box means.

The problem you are trying to do is abc + ac

I would write that as (a AND b AND c) OR (a AND c)

abc is a single box as it represents the case where all three are true.

ac means that a AND c are both true but b can be either.  Because of this it will take two boxes.

But that does not mean that you will end up with three boxes shaded because one box is repeated.

Hope that helps.

Bob

and where will you put c ?

Look at post 17

Bob

?? Did you look at all my recent posts?

Bob

But what have you been told it is?  You must have been given a rule for it.  Or an example.

I'll come clean about this topic.

I did some Boolean algebra and propositional logic back in 1969ish.  DNF was not part of it.

So when I saw your question I thought I'd better leave it for someone who knew what it was.

A while later I looked it up on Wiki.  It seemed straight forward enough for me to blunder in with a reply.

Wiki says DNF is " it is an OR of ANDs " and all their examples look like this:

(a AND b) OR (c AND d) etc.

If that definition is correct then all your questions have that form already:

(not p AND not q) OR (q)

(p AND q) OR (NOT p AND NOT q AND r)

(a AND b AND c) OR (a AND b)

So I wondered if the questioner wanted FULL DNF or maybe NOT is dis-allowed.  But Wiki's examples include NOTs and anyway, some expressions could not be rendered in DNF if NOT was dis-allowed. 

If you are able to give the definition according to your course, maybe we can get somewhere.

Bob

hi dee93

Welcome to the forum. 

I thought (pq + r) meant (p AND q OR r) so now I'm confused as all these expressions appear to be in DNF already.  Have I got this wrong?

and then post again.  I'm fairly confident I can do the manipulations but what am I trying to achieve?

Bob