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Geek Culture / A bit of an interesting math problem

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Dark Java Dude 64
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Posted: 30th May 2013 09:57 Edited at: 30th May 2013 11:19
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Hello! Basically, I need a mathematical equation that can simulate a boolean AND function. Of course, I could simply use Q=AB for this, but I need an equation that does not use multiplication or division. The equation is allowed to use addition and subtraction, and division and multiplication are allowed, but only if by a constant. So following those rules, I just need an equation that will output a 1 only if both inputs are 1 and will output a 0 otherwise, basically just have a profile following the truth table of an AND gate.

Why do I need this? I don't wanna say quite yet, but you shall all find out soon.

Thanks!

Edit:
I have come up with a way to do what a I wanted to do without using an equation of sorts. Disregard!
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Wolf
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Posted: 30th May 2013 14:00
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Quote: "I have come up with a way to do what a I wanted to do without using an equation of sorts. Disregard! "


Yeah...but you are still going to tell us what you needed it for, right?

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Michael P
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Posted: 30th May 2013 19:18 Edited at: 30th May 2013 19:18
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Here is a lambda calculus definition that does what you want (if you say 0 = false and 1 = true). It might be of some use to you.


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Benjamin
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Posted: 30th May 2013 19:19 Edited at: 30th May 2013 19:20
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Quote: "I have come up with a way to do what a I wanted to do without using an equation of sorts. Disregard!"


Did you figure out a way with just addition and subtraction?

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Dark Java Dude 64
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Posted: 30th May 2013 22:54
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Quote: "Yeah...but you are still going to tell us what you needed it for, right?"
Well, for now I'll tell you this: I'm creating some mechanisms that do boolean logic based stuff.

Quote: "It might be of some use to you."
Ah, I'll definitely have to look into that!

Quote: "Did you figure out a way with just addition and subtraction?"
Haha well, due to commutative property of addition and such, I'm pretty sure it isn't possible with just addition and subtraction.

Basically, the solution I have thus far is to add both inputs, so when the two inputs added equal 2, I have a mechanism that will grab the output and pull it to high.

Building a mechanical AND gate is pretty easy, but I have some pretty specific requirements here for what I'm doing.
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Neuro Fuzzy
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Posted: 31st May 2013 00:40
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If you have an equation in the form:
a*A+b*B+c

with A and B being the inputs and a,b,c being constants (which, you have to have that form, since things like A-(B-A) reduce to that form), then:

c=0 (when A=B=0)
a*A+c=0 (when B=0)
b*B+c=0 (when A=0)
a*A+b*B+c=1

The first equation means c=0, the second means a=0, the third means b=0, the fourth gives a contradiction.

That said, floor(0.9*A+0.9*B) would work!


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Dark Java Dude 64
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Posted: 31st May 2013 01:18
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Ahah! Very interesting indeed! I'll have to figure out how to mechanically implement that floor function, but I already have some ideas. Thanks!
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Libervurto
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Posted: 31st May 2013 02:34
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(A=B)-(A=0) seems to work, but might be breaking your rules and it's basically (A+B)=2 anyway.

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Dark Java Dude 64
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Posted: 31st May 2013 04:45
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Ah, that does partially work... I don't quite recall but I think it outputs either -1 or -2 at some point, but sadly those can't be allowed.

I shall change the topic of this thread a bit, basically if anyone can figure out a way to use only XOR and NOT gates to make any other gate, that would be great. Based upon my own experimentation in Logisim, it seems impossible...

I have ways to create logic gates, but they aren't the greatest ways. I actually managed to create a working mechanical transistor, but it's not the easiest to assemble and doesn't seem like it would be reliable enough to go in the large project I want it to. I have other methods too which involve things connecting and disconnecting, and while definitely possible, I would rather things remain pretty static overall... But damn, I honestly never would have guessed coming up with designs for mechanical logic gates would be so hard! It's incredibly frustrating but also fun at the same time. Right now I need to decide if I'm going to go forward with what I have or if I want to come up with a better way to do things and go forward with that... I'm not looking for other people to give me designs with this paragraph, I'm just blabbing on. If anything, I want as much of this thing to be my own design as possible.
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Libervurto
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Posted: 31st May 2013 05:18
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If you send one of the inputs through a NOT then both through an XOR you have an equivalence testing gate. I even tested it in Minecraft -->

The difficulty in learning is not acquiring new knowledge but relinquishing the old.
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Dark Java Dude 64
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Posted: 31st May 2013 05:22 Edited at: 31st May 2013 05:32
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Indeed, problem is with really anything that uses the equivalence testing, you get a situation where the truth table is either



or



So, that's basically my issue.

Edit: I have come up with a way to use 3 equivalence testers to produce this circuit, but now I simply need a 3 input equivalence taster, but that shouldn't be hard at all.
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