Boolean Logic Design - Reduction

I have the following function to be reduced/simplified.

F(A,B,C,D) = BC + (A + C'D') where ' denotes the complement

Here's my solution: = BC + (A + C'D')' = BC + (A + (C+D) = BC + (A + C + D) = BC + C + A + D = C(B + 1) + A + D = C*1 + A + D = C + A + D

Is this correct?


As in traditional algebra, if you do something to one side of the equation, you must do it to the other side, including complementing. Here we state the original equation:

F'(A,B,C,D) = BC + (A + (CD)')

Since we have F' instead of F, my intuition tells me to complement both sides, but first I distribute the complement in the term (CD)' to make life easier in the long run:

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

Now we can complement both sides of the equation:

1: F = '(BC)'(A + (C'+ D')) The OR becomes AND after distributing complement

Now let's distribute the complements inside just to see what we get:

2: F = (B'+ C')(A'(CD))

Now we can just distribute the right term (A'(CD)) over the two terms being OR'ed:

3: F = B' (A'(CD)) + C' (A'(CD))

We see that the right term goes away since we have a CC' and thus we are left with:

4: F = A'B'CD

Hopefully I didn't make a mistake. I know you've found the answer, but others reading this might have a similar question and so I did it out to save duplicate questions from being asked. Good Luck!

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