I have to create the circuit for this function: A+(BC)'+(CD)'=Z, using NAND gates.
After asking some friends about how to do this, and searching in the forums, I been using this method:

Please note [' = NOT] and I am not simplifying the expression in the following:

AB+DA+CA+DCB

Double NOT the expression (because double NOT does not alter the expression):

(AB+DA+CA+DCB)''

Using DeMorgans (A+B)' = A'.B'

Therefore:

((A.B)'.(D.A)'.(CA)'.(DCB)')'

Which can be implemented using purely NAND gates.

You may be advised to look at simplifying the expression, although that depends on what your assignment requires.

Dave

So I got this:

Z= A + (BC)' + (CD)'

Z= [A+(BC)'+(CD)']''

Using De Morgan's...

Z=[A'.(BC)''.(CD)'']'

Then finally...

Z=[A'.(BC).(CD)]'

And I don't know what to do from now on, since (B.C) are AND, not NAND, what am I missing?

 

Put the NAND back into (BC) by double NOT gates.

(BC) = ((BC)')'

 

Thanks for the fast and accurate answer.
I made a diagram of the final circuit, is it ok?

 

Thanks for the fast and accurate answer.
I made a diagram of the final circuit, is it ok?

You final circuit doesn't use just NAND gates. You have inverters in there as well. You need to implement those with NAND gates, too. Also, you have a 3-input NAND. Be sure that that is acceptable since problems like this frequently only allow you to use 2-input NAND gates.

 

I tried to correct it, the function remains the same this way?

 

Nope. Look at your expression carefully. Does it match your circuit?