# Help with implement NAND circuit

#### mwl

Joined Sep 28, 2011
7
Hello dear members of AAC! I'm having problem with implement this circuit with ONLY 2 input - NAND ports:

F = ACD + AB + BC'

Also, I don't know if I can minize it. I tried, but I were stuck in the same point =//

Last edited:

#### Georacer

Joined Nov 25, 2009
5,182
Can you post your efforts, for us to see and comment on?

#### mwl

Joined Sep 28, 2011
7
Course!
Well, I tried to manualy minize it, but all i got was:

F = A(CD + B) + BC'

And that's all!

I'm really confused about the De Morgan's theorem, how to use it to design and draw a circuit only with the NAND ports. I know how to make an inversor, AND and OR ports from only NANDs, but I'm not sure if that is all that I need for this.

Also, I used a software called "Logic Friday" to minimize it, but it gave me the same logical function.

#### panic mode

Joined Oct 10, 2011
2,215
that is already minimized form
to make use of NANDs means to produce terms in form

(XY)'

in your case it would be something like

ACD+AB+BC'=
(ACD+AB+BC')"=
[((ACD)'(AB)'(BC')']'=
[((AC)"D)'(AB)'(BC')']'
etc.

note that (AC)' need to be inverted one more time before anding with D.

we can do the same to get around 2-input limitations for final gate. in example here that one is still using 3 inputs but you can finish it same way the rest was done (hint, read the note).

• mwl

#### mwl

Joined Sep 28, 2011
7
Thanks a lot for the answer!

From what I saw, you did this:

= (ACD+AB+BC')" First, you double negated all the equation
= [((ACD)'(AB)'(BC')']' After, used De Morgan,
[((AC)"D)'(AB)'(BC')']' And lastly, i didn't understand how you isolated AC from D.

#### Georacer

Joined Nov 25, 2009
5,182
It's nothing really: ACD=(AC)D=(AC)''D
because F=F''

• mwl

#### mwl

Joined Sep 28, 2011
7
Thanks a lot again! AAC > all!

#### mwl

Joined Sep 28, 2011
7
Also, if I can have another answer =)

I just put this equation into some map minimizer.

Entered:
F=x + x'z + x'w + z'w

And i got this:

Minimized:
F = x + z + w

Someone how what simplification should I do here?

#### Georacer

Joined Nov 25, 2009
5,182
Are you asking how the software got the final expression or how to implement F=x+z+w with a NAND gate?

If it's the latter, try to think of it like this: F=x+z+w=(x'z'w')'
and also: a NAND b NAND c = (a NAND b) NAND c.

Can you figure anything out?

#### mwl

Joined Sep 28, 2011
7
Sorry! I wasnt clear!
What I wanted to know is how the software got the final expression #### Georacer

Joined Nov 25, 2009
5,182
The software might have used a myriad of methods.

The most brain-dead and fool-proof (but not the shortest) method you can use, is to construct a truth table from the given expression and then find the Sum of Products solution, which is most of the time, the shortest.