# Confusing logic simplification problem

Discussion in 'Homework Help' started by SilverKing, Jun 5, 2014.

1. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
Hi everyone,

I've the following problem:

I didn't even know how to start with it, or more specific, I didn't even understand the objectives.
All what I could do is represent it as: (A'+B')C + A(B+C')

Let's begin with (a). Any hints?

2. ### timwhite Member

Apr 10, 2014
50
7
I think a solid hint would be to think about how you could apply De Morgan's laws here. The main goal would be to simplify the logic as much as possible.

I got it down to two terms.

3. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
If you are talking about (a), then tell me what does it mean to "divide the circuit into series and parallel connections"?

4. ### MrCarlos Active Member

Jan 2, 2010
400
134
Hello SilverKing

You formula (A '+ B') C + A (B + C ') seems correct.
now: giving a little push to paragraph (a):
(a) subdividing it into series and parallel connections of subcircuits until single switches are Obtained.

analyzes the image attached to separate switches trying to get a single switch.

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5. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
MrCarlos:

A' and C cannot be in series unless I ignore B', because there is an essential node between the three. The same thing for B' and C.

But if I merge A' and B' due they're in parallel, their equivalent can be in series with C. Or am I missing some thing?

6. ### djsfantasi AAC Fanatic!

Apr 11, 2010
2,900
876
Why not, if you duplicate C? A' and C in series with B' and C in series, and the two groups in parallel.

7. ### MrCarlos Active Member

Jan 2, 2010
400
134
Hello SilverKing

Yes correct
A 'and C can not be in series unless I ignore B' Because there is an essential node Between the three.
but. . . to accomplish this:
subdividing it into series and parallel connections of subcircuits until single switches are Obtained.
We need to "forget" That, there is an essential node Between the three.

I Believe!.

8. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
djsfantasi
Then, the equation would be: A'C+B'C+AB+AC'. Simplifying it: A+C

So?

Last edited: Jun 15, 2014
9. ### djsfantasi AAC Fanatic!

Apr 11, 2010
2,900
876
So you have simplified the circuit into single switches. (I'd draw the schematic). Now, solve parts b and c and show they are all the same.

10. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
I guess (b) is the same as (a). And for (c), I have to convert A'C+B'C+AB+AC' from Sums-of-Products form to Product-of-sums form, isn't?

Last edited: Jun 6, 2014
11. ### djsfantasi AAC Fanatic!

Apr 11, 2010
2,900
876
Guess? Show your work (I should have mentioned that before). And why do you think you need a Product of Sums?

12. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
Sorry for being late.

"ANDing the OR terms together" = Product of sums.
"ORing the and terms togeher" = Sum of products.

13. ### djsfantasi AAC Fanatic!

Apr 11, 2010
2,900
876
Ok, you understand the difference between SOP and POS. But why do you need the POS form? For part A, how did you arrive at A+C (show your work)? And how is that the answer to (b)?

Hope you understand that all of these questions are because this is the Homework Help forum; not Homework Done for You forum.

14. ### SilverKing Thread Starter Member

Feb 2, 2014
72
0
Answering your questions: I think that I need POS because the objective is to form OR terms and ANDing them together.

For part (a): from A'C+B'C+AB+AC'

We get: A+C

I think the answer of (a) would be the same as (b), because it's in SOP form.

15. ### BR-549 Well-Known Member

Sep 22, 2013
2,177
416
I believe the answer is (A AND B OR C') OR (A' OR B' AND C) is true.