4 ms·

Ask HN: Why is binary used instead of ternary?

4 points by niche 12y ago

Is ternary not the next logical step in computing?

alain94040 12y ago
If you think in terms of voltage on a pin, how you would implement ternary? Binary is simple: 0V, or 5V (at least a long time ago...). Transitioning from one state to the other is obvious. How would you do it with ternary logic?
- niche 12y ago
  Well there are so many options here, which make things that much more exciting. So basically: 0V, 5V, everything else :-)
- niche 12y ago
  You could have predefined gates 0V-1V= 0 1V-2V= 1 2V-3V= 2 / -1 Do negative voltages exist? Positive voltage, negative voltage, no voltage Ternary allows for measurements of relativity at the pin level whereas binary is a yes/no...
victorhn 12y ago
log2(n) == c * log3(n)
jeffwass 12y ago
I think I heard this in a Unix fortune 15 years ago : When engineers implement base-4 logic, will they call it quits?
kedean 12y ago
It's completely possible, but it's just not worth it. The information density of ternary is higher than binary, sure, but you now need 3 states to represent it. This applies to ternary vs base 4, and so on. As it turns out, it's been proven that binary has the optimal ratio of info density to symbols, and any higher of a base gives you no net benefit. Unfortunately I don't have a link to the proof on hand, but if someone else does I'd appreciate it. We would also lose decades of knowledge on binary operations and how best to do it. Two's complement is out the window, for instance. Additionally, the entire CS mindset is built around boolean logic. Exclusive-or, for instance, makes no sense when you remove binary operation. There's not much to gain from it either, since any sort of ternary operation can be implemented as a binary operation without that much overhead.
- mcshaner1 12y ago
  I think the optimal base is actually the natural log e, or about 2.71. I saw a derivation of this before but can't find the reference. Ternary actually comes about a bit better from an information density standpoint, but all the other points you made about difficulties with base 3 and benefits of base 2 still stand.
  - kedean 12y ago
    Good point, 2 is the optimal integer base.
mathgeek 12y ago
Stack Overflow already has a great thread on this very question. http://stackoverflow.com/questions/764439/why-binary-and-not-ternary-computing http://stackoverflow.com/questions/764439/why-binary-and-not...
lazylester 12y ago
OK, let's try ternary. Oh, why not go to quaternary, or quinary (I mighta made that word up), and so on. Before you know it, we're back to analog!
niche 12y ago
nob: not only binary 10W "1" "0" "Whatever" (not to be mistaken for power measurement) Could a binary computer teach itself to build ternary circuits? Base(4) is effectively base~2, base_e is purportedly optimal, base`pi is compelling Is 3 a concept best grasped by humans? binary within ternary or ternary within binary?

4 points by niche 12y ago

Is ternary not the next logical step in computing?

If you think in terms of voltage on a pin, how you would implement ternary? Binary is simple: 0V, or 5V (at least a long time ago...). Transitioning from one state to the other is obvious. How would you do it with ternary logic?

niche 12y ago
Well there are so many options here, which make things that much more exciting. So basically: 0V, 5V, everything else :-)
niche 12y ago
You could have predefined gates 0V-1V= 0 1V-2V= 1 2V-3V= 2 / -1 Do negative voltages exist? Positive voltage, negative voltage, no voltage Ternary allows for measurements of relativity at the pin level whereas binary is a yes/no...

victorhn 12y ago

log2(n) == c * log3(n)

jeffwass 12y ago

I think I heard this in a Unix fortune 15 years ago : When engineers implement base-4 logic, will they call it quits?

kedean 12y ago

It's completely possible, but it's just not worth it. The information density of ternary is higher than binary, sure, but you now need 3 states to represent it. This applies to ternary vs base 4, and so on. As it turns out, it's been proven that binary has the optimal ratio of info density to symbols, and any higher of a base gives you no net benefit. Unfortunately I don't have a link to the proof on hand, but if someone else does I'd appreciate it. We would also lose decades of knowledge on binary operations and how best to do it. Two's complement is out the window, for instance. Additionally, the entire CS mindset is built around boolean logic. Exclusive-or, for instance, makes no sense when you remove binary operation. There's not much to gain from it either, since any sort of ternary operation can be implemented as a binary operation without that much overhead.

mcshaner1 12y ago
I think the optimal base is actually the natural log e, or about 2.71. I saw a derivation of this before but can't find the reference. Ternary actually comes about a bit better from an information density standpoint, but all the other points you made about difficulties with base 3 and benefits of base 2 still stand.
- kedean 12y ago
  Good point, 2 is the optimal integer base.

mathgeek 12y ago

Stack Overflow already has a great thread on this very question. http://stackoverflow.com/questions/764439/why-binary-and-not-ternary-computing http://stackoverflow.com/questions/764439/why-binary-and-not...

lazylester 12y ago

OK, let's try ternary. Oh, why not go to quaternary, or quinary (I mighta made that word up), and so on. Before you know it, we're back to analog!

niche 12y ago

nob: not only binary 10W "1" "0" "Whatever" (not to be mistaken for power measurement) Could a binary computer teach itself to build ternary circuits? Base(4) is effectively base~2, base_e is purportedly optimal, base`pi is compelling Is 3 a concept best grasped by humans? binary within ternary or ternary within binary?