Boolean Identities

Discussion in 'Homework Help' started by JasonL, Dec 3, 2012.

  1. JasonL

    Thread Starter Active Member

    Jul 1, 2011
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    0
    How do I simply AB + BC + AC' + BCD using boolean identities?
    Using a K-map I know the answer is AC' + BC.

    This is what I did so far
    AB + BC + AC' + BCD
    AB + AC' + BC(1+D)
    AB + AC' + BC
    I don't know how to simplify using identities beyond this point.
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,747
    4,796
    Q1) Given what you've got so far, which of the three terms needs to be made to disappear?

    Q2) Can you start from the other two terms (i.e., the answer) and figure out how to produce the third term? Sometimes this is much easier to do. If so, then to that carefully and then just reverse the steps to go the other way.

    Hint: How can you take f(X,Y,Z) = XY and turn it into two terms each of which involved X, Y, and Z (or, of course, their complement)?
     
  3. JasonL

    Thread Starter Active Member

    Jul 1, 2011
    47
    0
    Thanks! I expanded AB
    AB + BC + AC'
    ABC + ABC' + BC + AC'
    BC(A+1) + ABC' + AC'
    BC + AC'(B+1)
    BC + AC'
     
  4. WBahn

    Moderator

    Mar 31, 2012
    17,747
    4,796
    Great.

    In doing your write up, include the step

    AB + BC + AC'
    AB(C+C') + BC + AC' <----
    ABC + ABC' + BC + AC'

    So that your reasoning is obvious.
     
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