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Quick logic questions

  1. Jan 4, 2015 #1

    Zondrina

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    Homework Helper

    1. The problem statement, all variables and given/known data

    1. Reduce the following logical expression to four literals and draw a gate level circuit, which implements the result.

    $$AB + BCD + BC + A \bar C$$

    2. Simplify the following:

    $$(A + \bar B C)(B + C)(B + \bar C)$$

    2. Relevant equations


    3. The attempt at a solution

    I would just like to verify I understand.

    Here is my working for part 1:

    Screen Shot 2015-01-04 at 2.16.31 PM.png

    For part 2 here's what I came up with:

    $$(A + \bar B C)(B + C)(B + \bar C)$$
    $$= (A + \bar B C)(B + C \bar C)$$
    $$= (A + \bar B C)(B + 0)$$
    $$= (A + \bar B C)B$$
    $$= AB + \bar B B C$$
    $$= AB + 0C$$
    $$= AB + C$$

    I think that's as simple as it can become.

    Thank you.
     
  2. jcsd
  3. Jan 4, 2015 #2

    berkeman

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    Staff: Mentor

    A good way to check your work is to draw the Karnaugh Maps and see if the simplest grouping of terms matches your equation manipulations. Can you show us the corresponding K-Maps for this question? :-)
     
  4. Jan 4, 2015 #3

    Zondrina

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    I have a few more pages before I get to K-Maps today. I actually just started this subject so I don't know much, but I'm working on it.
     
  5. Jan 4, 2015 #4

    berkeman

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    Staff: Mentor

    You are going to like K-Maps! :-)
     
  6. Jan 4, 2015 #5

    berkeman

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    Staff: Mentor

    BTW, I got a different answer for part 1) using a K-Map. I'd be interested in seeing what you get using that method when you get to it.
     
  7. Jan 5, 2015 #6
    Note for Q2 that 0C = 0
     
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