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)

 

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

 

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

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)'?

 

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.

 

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.

 

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.

 

Of course, my bad.
(Damn, I had a streak there)