# Help with implement NAND circuit

Discussion in 'Homework Help' started by mwl, Oct 12, 2011.

1. ### mwl Thread Starter New Member

Sep 28, 2011
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0
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: Oct 12, 2011
2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Can you post your efforts, for us to see and comment on?

3. ### mwl Thread Starter New Member

Sep 28, 2011
7
0
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.

4. ### panic mode Senior Member

Oct 10, 2011
1,328
305
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 likes this.
5. ### mwl Thread Starter New Member

Sep 28, 2011
7
0
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.

6. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
It's nothing really: ACD=(AC)D=(AC)''D
because F=F''

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7. ### mwl Thread Starter New Member

Sep 28, 2011
7
0
Thanks a lot again!
AAC > all!

8. ### mwl Thread Starter New Member

Sep 28, 2011
7
0
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?

9. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
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?

10. ### mwl Thread Starter New Member

Sep 28, 2011
7
0
Sorry! I wasnt clear!
What I wanted to know is how the software got the final expression

11. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
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.