# Circuit Challenge: Invert Three Signals With Only Two Inverters

Discussion in 'General Electronics Chat' started by MrAl, Sep 22, 2015.

1. ### MrAl Thread Starter Distinguished Member

Jun 17, 2014
2,542
511
Hello there,

Here is a circuit challenge if you feel up to the task.

We have three inputs A,B,C, and three outputs which must be the invert of the three inputs, so the outputs would be A', B', C'. Normally we would just hook up three inverters, one inverter for each line, so that the three inputs get inverted, and we are done.
But this challenge requires that you can only use two inverters and any number of AND and OR gates, but NOTHING else. The three outputs must be the inputs inverted.
To illustrate the more typical circuit with three inverters:
A---|>o---A'
B---|>o---B'
C---|>o---C'

That circuit uses three inverters as shown, but the challenge circuit can only use two and also any number of AND and OR gates.
To answer any possible question about NAND and NOR gates, the answer is "NO", you can not use any NAND or NOR or XOR or anything else, just AND and OR are allowed (along with the two inverters).
Also, no time multiplexing allowed either, it has to be a standard combinatorial logic circuit.

2. ### MrAl Thread Starter Distinguished Member

Jun 17, 2014
2,542
511
Hello again,

No takers out there?

As of my reading of this thread today, 61 views but no replies :-(

3. ### Dodgydave AAC Fanatic!

Jun 22, 2012
5,130
766
Well show us your way first, then we'll have a look...

4. ### #12 Expert

Nov 30, 2010
16,655
7,293
Apparently there is a lack of people who want to spend their time on a puzzle that doesn't solve any real need.

5. ### AnalogKid Distinguished Member

Aug 1, 2013
4,676
1,294
This puzzle dates back to the 50's 0r 60's. I solved it in school for extra credit a long time ago, but I can't go digging for the solution right now. I remember it in general. The big clue is the *unlimited* number of AND and OR gates. As I recall, a dozen or more.

ak

6. ### MrAl Thread Starter Distinguished Member

Jun 17, 2014
2,542
511
Hello there,

Well i think what you mean is it doesnt solve any practical engineering problem. That is probably right. But also that may not be the specific 'need' either. This problem is more for educational purposes and shows something interesting about binary logic.

What is interesting is the implications of having only two states for a variable, as it reduced the total number of cases so much that it can greatly simplify the circuit and defining equations. A real simple illustration is as follows...

Say we have a ball that can be any of five different colors, red, blue, yellow, green, orange.
We ask the question, "Is the ball red?"
If the answer is "Yes", then we know the ball is red, but if the answer is "No", then we dont know what color it is yet, as it can be any of the four remaining colors.

But if we only have two different colors, red and blue (binary) and we ask the same question, if the answer is "Yes" then we know it is red, and if the answer is "No", then we know the color is blue. So either way we know what color the ball is, even though the first guess was not correct. That is because now we have:
red'=blue
or:
blue'=red

so even when we know what the 'not' color is we know what the actual color is.

The simplifications that come about because of this simple fact (only two states) are very interesting and help to clarify problems in logic.

I dont know if it will do any good to post the solution or not because probably no one will want to try to trace out the circuit and see how or why it works. And yes there are many gates involved and only two inverters. I'll wait a bit more before posting.

7. ### Dodgydave AAC Fanatic!

Jun 22, 2012
5,130
766
Nobody has answered it, because s nobody is interested..

8. ### peter taylor Member

Apr 1, 2013
106
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That's cheating !

Roderick Young likes this.
9. ### jpanhalt AAC Fanatic!

Jan 18, 2008
5,699
909
Is it safe yet to give an answer without moderator or member criticism?

John

10. ### AnalogKid Distinguished Member

Aug 1, 2013
4,676
1,294
On *this* forum, reasonably safe. Besides (channeling an old joke), now that you're here we have them outnumbered.

ak

11. ### shortbus AAC Fanatic!

Sep 30, 2009
4,082
1,663
When it comes to the use of logic circuits today, I'll say what most people have told me; use a micro controller.

GopherT likes this.
12. ### eetech00 Active Member

Jun 8, 2013
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So you can build it without using ANY inverters

shortbus likes this.
13. ### Roderick Young Member

Feb 22, 2015
408
168
Puzzles are worthwhile, if only to stimulate the mind. But more deeply, they could inspire us to new ways of doing things in the future.

I gave your puzzle a try, but did not succeed.

Nov 13, 2010
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15. ### Roderick Young Member

Feb 22, 2015
408
168
There's a hint of depth in your statement. If you could make 3 inverters out of 2, you could in theory make any number of inverters out of 2. It's like if I could instantly turn \$2 into \$3, I could be as rich as I wanted. And in fact, that's the case (the part about the inverters, not the dollars).

Apr 1, 2013
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