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?

 

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.

 

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

 

Hello SilverKing

You formula (A '+ B') C + A (B + C ') seems correct.
now: giving a little push to paragraph (a):
The full statement reads:
(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.

 

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?

 

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.

Why not, if you duplicate C? A' and C in series with B' and C in series, and the two groups in parallel.

 

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!.

 

djsfantasi
Then, the equation would be: A'C+B'C+AB+AC'. Simplifying it: A+C

So?

 

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.

 

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?

 

Guess? Show your work (I should have mentioned that before). And why do you think you need a Product of Sums?

 

Sorry for being late.

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

 

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.

 

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.

 

I believe the answer is (A AND B OR C') OR (A' OR B' AND C) is true.