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Full Adder Sum Formula (Logic)

  1. May 19, 2009 #1
    Hi,
    I've been trying to work out the formula for the sum for the full adder logic, however have come across a gap which I don't know how to fill.
    S = (¬A.¬B.C) + (¬A.B.¬C) + (A.¬B.¬C) + (A.B.C)
    S = ¬A.(¬B.C + B.¬C) + A.(¬B.¬C)
    S = ¬A.(B [tex]\oplus[/tex] C) + A.( do not know what to do at this point to reach the next stage
    S = (A [tex]\oplus[/tex] B) [tex]\oplus[/tex] C

    Does anyone know how to get to that last statement?

    Thanks for any help.
     
    Last edited: May 19, 2009
  2. jcsd
  3. May 19, 2009 #2

    berkeman

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    Staff: Mentor

    It's probably easiest to draw a Karnaugh map for the function, and use that to help your intuition in the reduction. Have you drawn a K-map for this yet?
     
  4. May 20, 2009 #3
    Nope. I have never used one before.

    Edit: How come this received a warning? This isn't homework or coursework. It's just studying.
     
  5. May 20, 2009 #4

    berkeman

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    Staff: Mentor

    Studying is coursework. Even if it's for self-study, it belongs in the Homework Help forums, and needs to follow the rules here. You can check out the Rules link at the top of the page for clarification.

    The K-map is a great tool for helping you visualize logic reduction. Here's an intro to get you started -- there are lots of other learning resources for K-maps on the web:

    http://en.wikipedia.org/wiki/Karnaugh_map

    .
     
  6. May 21, 2009 #5
    That doesn't make sense since every thread in these forums is about help to understand something, so one could always link it to a course since there are courses for everything, and thus everything should therefore be in the Homework Help forums. But anyway...

    Does anyone know how to solve this without the K-map since I don't really have colouring pencils to create this diagram, just a pen? Also, how would one solve this algebraically?
     
  7. May 21, 2009 #6

    Defennder

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    Homework Helper

    Why do you need coloured pencils for the Karnaugh map?
     
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