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Simplifying this equation using Boolean Algerbra

  1. Sep 28, 2011 #1

    Ese

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    1. The problem statement, all variables and given/known data
    Where
    . or SPACE (" ") = AND
    + = OR
    ` = NOT (Complementary)


    2. Relevant equations
    I've been having problems with the second question of my assignment. Here's the equation:
    [( a + bc ) + ( b` + a'c )]' = F


    3. The attempt at a solution
    So far, all I've done is this:
    [( a + bc ) + ( b` + a'c )]'
    = [(aa+ac+ba+bc) + (b'b' + b'c + a'b' + a'c)]'
    = [a+...

    Now I'm stuck. Please help me out. :(
     
  2. jcsd
  3. Sep 29, 2011 #2

    ehild

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    Homework Helper
    Gold Member

    Is it [( a + bc ) + ( b' + a'c )]'?

    I do not understand what you did. Try to simplify the expression between the square brackets. Do you know the relation a+a'c=a+c? Do you know De Morgan's laws?

    ehild
     
  4. Sep 29, 2011 #3

    Ese

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    I tried this:

    = [(aa+ac+ba+bc) + (b'b' + b'c + a'b' + a'c)]'
    = [a+...

    [( a + bc ) + ( b` + a'c )]' = F
    = (a+bc)' + (b'+a'c)'
    = (a'+(bc)') + (b+(a'c)')
    = a.b'c' + b'.ac'
    = ab'c' + b'ac'
    = ab'c'

    Is this correct?
     
  5. Sep 29, 2011 #4
    One thing you did wrong was that you forgot to change the symbols for the " ' " equations

    ex: (a + b)' = a'b'

    So, for your first couple lines:

    [( a + bc ) + ( b` + a'c )]'

    = (a+ bc)'(b'+ a'c)'
    = (a'(bc)')(b(a'c)')
    = ............
     
    Last edited: Sep 29, 2011
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