Hello. I'm trying to remember Boolean algebra and De Morgan's laws. And I have a problem with implementing an XOR gate using NAND gates. Especially with the transformation Q=A+B= ??? I am attaching a combination of NAND gates that create an XOR gate I would be grateful if someone helped...

Where's the addition here, just looking at the diagram? By adding a few symbols, you can define logical states at various points in the system: Q1 = ~(A*B) Q2 = ~[A*~(A*B)] = ~(A*Q1) Q3 = ~ = ~(B*Q1) Q = ~(Q2*Q3) = ~{~[A*~(A*B)]*~ }

It's not that simple, friends, Regards. PS: Sorry for the quality, but everyone should be able to understand it.

Since there is an imposed type of gates from which you build...

These gates are NANDs, not NOTs.

No, it's not adding, it's expansive XOR gate designation. Thank you so much for help

Implementing an XOR Gate Using NAND Gates: De Morgan's Laws and Boolean Algebra

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#1 12724444 11 Sep 2013 17:17

MMG MMG

Level 10

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Post #1
12724444 11 Sep 2013 17:17

Hello.
I'm trying to remember Boolean algebra and De Morgan's laws.

And I have a problem with implementing an XOR gate using NAND gates.
Especially with the transformation Q=A+B= ???

I am attaching a combination of NAND gates that create an XOR gate

I would be grateful if someone helped me
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#2 12724616 11 Sep 2013 18:12

fuutro fuutro

Level 43

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Post #2
12724616 11 Sep 2013 18:12

Where's the addition here, just looking at the diagram?

By adding a few symbols, you can define logical states at various points in the system:
Q1 = ~(A*B)
Q2 = ~[A*~(A*B)] = ~(A*Q1)
Q3 = ~[B*~(A*B)] = ~(B*Q1)
Q = ~(Q2*Q3) = ~{~[A*~(A*B)]*~[B*~(A*B)]}

http://pl.wikipedia.org/wiki/Prawa_De_Morgana
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#3 12724636 11 Sep 2013 18:18

13adam13 13adam13

Level 29

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Post #3
12724636 11 Sep 2013 18:18

It's not that simple, friends,

Regards.
PS: Sorry for the quality, but everyone should be able to understand it.
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#4 12724653 11 Sep 2013 18:23

fuutro fuutro

Level 43

» | Helpful post? (+3)

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Post #4
12724653 11 Sep 2013 18:23

Since there is an imposed type of gates from which you build...
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#5 12724660 11 Sep 2013 18:24

13adam13 13adam13

Level 29

» | Helpful post? (+1)

Post #5
12724660 11 Sep 2013 18:24

These gates are NANDs, not NOTs.
#6 12725235 11 Sep 2013 20:27

MMG MMG

Level 10

» | Topic author Helpful post? (+1)

Post #6
12725235 11 Sep 2013 20:27

fuutro wrote:
Where's the addition here, just looking at the diagram?

By adding a few symbols, you can define logical states at various points in the system:
Q1 = ~(A*B)
Q2 = ~[A*~(A*B)] = ~(A*Q1)
Q3 = ~[B*~(A*B)] = ~(B*Q1)
Q = ~(Q2*Q3) = ~{~[A*~(A*B)]*~[B*~(A*B)]}

http://pl.wikipedia.org/wiki/Prawa_De_Morgana

No, it's not adding, it's expansive XOR gate designation.

Thank you so much for help
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