Confusing logic simplification problem

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

  1. SilverKing

    Thread Starter Member

    Feb 2, 2014
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    Hi everyone,

    I've the following problem:

    [​IMG]

    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
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    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
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    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):
    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.
     
  5. SilverKing

    Thread Starter Member

    Feb 2, 2014
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    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
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    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
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    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
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    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
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    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
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    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
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    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
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    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
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    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
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    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'

    [​IMG]

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