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Math Help - Reduce

  1. #1
    Member
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    May 2010
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    Reduce

    Hello, my head hurts. I'm trying to reduce this:

     M=A(B+C+B\bar{C})+ B(A \bar{C}+AB)+ BC+AB\bar{C}+(\bar{A}+C)
    the last part (\bar{A}+C)should also have a \bar around the whole thing but i couldnt get that to work in tex.

    I got this far:

     AB + AC + BC + AB\bar{C} + AB\bar{C} B\bar{A}C + BAB + A + \bar{C}<br />
= B(A + C + A\bar{C} + A\bar{C} + \bar{A}C + AB) + AC + A + \bar{C}

    But im not sure if this is correct, if it is, hints for further reducing is very welcome
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  2. #2
    MHF Contributor
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    I'll write A' for \bar{A}, and similarly for other variables.

    \overline{\bar{A}+C}=A\bar{C}. So, by using distributivity and eliminating the same minterms, or disjuncts (AB and twice ABC'), we get

    AB + AC + ABC' + BC + AC'

    Next, ABC' + AC' = AC'(B + 1) = AC', so we have

    AB + AC + BC + AC'

    AC + AC' = A, and A + AB = A, so the result is A + BC.
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  3. #3
    Member
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    May 2010
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    aha \overline did the trick

    I've totally missed the obvious fact that X and X' eliminate eachother, it's been a long day, and i thank you
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