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Boolean algeabra prblem using T8/T8' distributivity theorems

  1. Sep 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Convert each of the equations to an equivalent 2 - level implementation using t8/t8' distributivity theorems to get SOP/POS form. Simplify
    F= Z((W'+Y+X')(W'+XY'Z))
    G= ABC+D'(B+AC)(A'+C)'


    2. Relevant equations
    T8: x*(y+z)= x*y+x*z
    T8': x+(y*z)=(x+y)*(x+z)



    3. The attempt at a solution

    I used T8' to take out w':
    F=Z(W'+(X'+Y)(XY'Z))
    =Z(W'+X'XY'Z+XYY'Z)
    =Z(W'+0+0)
    =Z*W


    G= ABC+D'(B+AC)(A'+C)'

    I distribute D' using T8:
    ABC+(BD'+ACD')(A'D'+CD')'

    but then do I continue as:
    ABC+A'BD'D'+BC'D'D''+AA'CD'D'+ACC'D'D''
    =ABC+A'BD'+BC'(0)+(0)CD'+A(0)(0)
    =ABC+A'BD'+0+0 (x*x'=0; x*x=1; x*0=0)
    =ABC+A'BD'
     
  2. jcsd
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