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Achievement Unlocked: Beyond Binary

A project log for Tern - Ternary Logic Circuits

A series of ternary logic gates and higher level components implemented in the real world.

mechanical-advantageMechanical Advantage 08/24/2015 at 08:350 Comments

Nice! I stumbled onto this one by accident. It turns out that the XOR gate is as simple as removing the final pair of comparators from the end of the XNOR I already built. If you think about it, this is *really* obvious. An XNOR is a Negated XOR, so just stop negating it and you have an XOR gate. Here's the schematic.

This is the ternary XOR most strictly adherent to it's binary counterpart according to Kleene logic. It corresponds to the binary connective "Exclusive Disjunction". Due to the expansive possibilities of ternary logic, there are several different truth tables which could have a claim to being the true "Ternary XOR". For example, this gate does not calculate the sum of two trits, while the binary XOR does calculate the sum of two bits. I am arbitrarily selecting this XOR as *the* XOR because Kleene logic says so. It's a straight-up appeal to authority.

And with this gate finished, I have now demonstrated and documented the strictest ternary equivalent of every two-input binary gate possible. From here on out, any two-input gates devised are going to be pushing the boundary of what is even capable of being represented in a binary system. There's still a lot of work to be done (multiplexors, latches, adders, multipliers, etc.) that has already been done with binary circuits, but this project is now at the point where the potential benefits of ternary will actually have a chance to be demonstrated. The point is not to solve every problem of computing by just adapting existing binary circuits to a ternary system. The point is to solve some computing problems in entirely new ways that binary cannot even approximate.

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