__ _______ ___ Find the complement of F = (A,B,C,D) = BC (A + CD) and reduce it.

Question

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Find the complement of F = (A,B,C,D) = BC  (A + CD)   and reduce it. Then, implement the simplified expression using AND, OR, and NOT gates.

PS. Sorry about the underscores its the only way i could format the problem.

I want to learn how to do this problem because a similar will probably be on the exam.

So far I have:

(BC)' (A + (CD)')'    (I translated it from the underscore, was this the right translation?)

= (B' + C') (A' * (C' + D')'

= (B' + C')(A+(CD))

= AB' + B'CD + AC' + C'D     

I am not sure if I am correct or if I am close. If someone could help me with this problem that would be great. I am trying to learn the answer not just obtain the answer, so if you could please show your work. Thanks!

Explanation / Answer

if u mean F as below. then answer will be as follows.

F = (B' + C')(A+ (C' +D')'

let say B'+C' = K => K' = (B'+C')' = B'' C'' = BC
C'+D' = P
(A+C'+D')' = (A+P)'

now complement of F is

F = K(A+P)'
F' = (K(A+P)')' = K' + (A+P)'' = K' + (A+P) = BC+ A + C'+D'

F' = BC+A+C'+D'
F' = (B+C')(C+C') + A + D'   since C+C' = 1
F' = (B+C') + A + D'

F' = B+C'+A+D'

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