# 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
1,857
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.