Simplifying a Boolean Function: Is This the Correct Solution?

[kachilous]

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?

 

[Zryn]

Is the 1st line wrong or is the original equation wrong? There's an extra complement in there at the end.

Is the 2nd line complete? There's at the very least a bracket missing.

De Morgans Law: A'B' = A' + B'

 

[kachilous]

on the second step, I did De Morgans

 

[Mark44]

We got that, but the first line of your work doesn't follow from the problem statement.
Zryn was asking about the last complement below. It shouldn't be there.
BC + (A + C'D') is not equal to BC + (A + C'D')' <--- this one

 

[kachilous]

My apologies. The function should actually be F'(A,B,C,D) = BC + (A + (CD)')

 

[Mark44]

Why do you have F'(A, B, C, D)? I.e., F'?

 

[kachilous]

because I took the complement of the function F. So I'm reducing F'

 

[Mark44]

You aren't supposed to take the complement of the function - just write its formula in the simplest form. Am I missing something here?

 

[Zryn]

Perhaps you could write the original question verbatim and we can start again with your reasoning and results?