Boolean Algebra Help

Discussion in 'Math' started by chengie.teo, Feb 15, 2011.

  1. chengie.teo

    Thread Starter New Member

    Feb 15, 2011
    3
    1
    Hi,


    Can anybody guide me on how to simplified the expression
    1) (A'.B.C.D.E.F'.G.H) + (A+B+C+D+E+F'+G+H)
    and
    2) (A'.B.C.D.E.F'.G.H) . (A+B+C+D+E+F'+G+H)
     
  2. haykp

    New Member

    Oct 7, 2010
    18
    0
    This is the solution:
    1) (A'.B.C.D.E.F'.G.H) + (A+B+C+D+E+F'+G+H)
    (A'.B.C.D.E.F'.G.H) = A + (B.C.D.E.F'.G.H)' = A + B' +(C.D.E.F'.G.H)'
    putting this in up equation gives:
    A + B' +(C.D.E.F'.G.H)' + (A+B+C+D+E+F'+G+H) = A + A +B' +B + (C.D.E.F'.G.H)' + C+D+E+F'+G+H = A + 1 + (C.D.E.F'.G.H)' + C+D+E+F'+G+H = 1
     
  3. bitrex

    Member

    Dec 13, 2009
    79
    4
    How did you get (A'.B.C.D.E.F'.G.H) = A + (B.C.D.E.F'.G.H)'? Wouldn't it need to be (A'.B.C.D.E.F'.G.H)' = A + (B.C.D.E.F'.G.H)'?
     
    haykp likes this.
  4. chengie.teo

    Thread Starter New Member

    Feb 15, 2011
    3
    1
    Ya. That is the confusing part. In another post you show me that
    A.B not= (A'+B') but from this post you seems to be complementing the expression and work on it.
     
    haykp likes this.
  5. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    I, too, believe that haykp is wrong.

    I will use the identities (a*b*...*z)+w=(a+w)*(b+w)*...*(z+w)
    and w*(a+b+...+z)=w*a+w*b+...+w*z

    That said, we have:
    (A'.B.C.D.E.F'.G.H) + (A+B+C+D+E+F'+G+H)=
    (A'+A+B+C+D+E+F'+G+H)*(B+A+B+C+D+E+F'+G+H)*...*(H+A+B+C+D+E+F'+G+H)=
    1*(B+C+D+E+F'+G+H)

    and

    (A'.B.C.D.E.F'.G.H) . (A+B+C+D+E+F'+G+H)=
    A.A'.B.C.D.E.F'.G.H+B.A'.B.C.D.E.F'.G.H+...+H.A'.B.C.D.E.F'.G.H=
    0+A'.B.C.D.E.F'.G.H

    If someone thinks different, please correct me.
     
    haykp likes this.
  6. haykp

    New Member

    Oct 7, 2010
    18
    0
    Ooopsss....
    My fault, yes I agree the I wrote a wrong expression in my answer. Please sorry folks.

    I liked Georacer answer, very nice solution!!

    Just one thing in his answer, my belief that in the final result of the first expression the "A" variable should be included also i.e.

    (A'.B.C.D.E.F'.G.H) + (A+B+C+D+E+F'+G+H)=1*(A+B+C+D+E+F'+G+H)

    Please correct me if I wrong.
     
  7. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Of course, my bad.
    (Damn, I had a streak there)
     
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