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Boolean Algebra Help

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Simplify the following expressions using Boolean Algebra.

    a) A + AB (A or A and B)
    b) A'BC + AC (A(not) and B and C or A and C)
    c) A'B + ABC' + ABC (A(not) and B or A and B and C(not) or A and B and C)

    2. Relevant equations
    Some simple boolean algebra rules.
    x+1=0
    x*x=x
    x*x'=0


    3. The attempt at a solution

    For a, I got the answer of A.
    I did:
    A(1 + B)
    A(1)
    = A

    For b, I got the answer AC.

    I did:
    C(A'B + A)
    C(0 + A)
    = AC

    For c, I got the answer AB.
    I did:
    B(A' + AC' + AC)
    B(A' + (A.C') + (A.C))
    B(A' + (0) + A)
    B(A' + A)
    B(A)
    = AB

    Are my calculations correct or am I completely wrong? Thank you for your help.
     
  2. jcsd
  3. Sep 13, 2010 #2

    vela

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    Staff Emeritus
    Science Advisor
    Homework Helper
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    Looks good.
    How did you replace A'B with 0?
    It's not clear what you did from the second to third line, and you simplified A'+A incorrectly.
    When you have only a few variables, it's easy enough to verify that you simplified an expression correctly by writing out the truth table. For example, for A'BC+AC, you get
    Code (Text):
    A B C   A'  A'BC   AC    A'BC+AC
    T T T   F     F     T       T
    T T F   F     F     F       F
    T F T   F     F     T       T
    T F F   F     F     F       F
    F T T   T     T     F       T
    F T F   T     F     F       F
    F F T   T     F     F       F
    F F F   T     F     F       F
    Comparing the columns for AC and A'BC+AC, you can see they're not equal, so you know something went wrong in the simplification.
     
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