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That seems unlikely so long as we’re using electronic computers.
Right now, using binary  and a 3.3 volt system  you only have to say: Is this voltage bigger than 1.65 or less than that?…and you know whether you have a zero or a one.
A single transistor does the job  if the voltage you’re getting isn’t quite zero and it’s not quite 3.3 volts  a simple transistor amplifier can boost the voltage to being either exactly zero or exactly 3.3v.
In a base 3 (ternary) system, you need much more logic  you have to detect two thresholds  not one…and a simple amplification step won’t fix voltages that have degraded.
So ternary systems are not as compact as binary systems.
Furthermore  in a 3.3v system, you can tolerate just under 1.65 volts of noise or voltage drop and a one will still be a one and a zero still a zero. In a ternary system, you have to split the voltage range into three  so you have 0, 1.65 and 3.3 as your zero, one and two voltages  which means that the thresholds are down to 0.835 volts. Your system is only half a tolerant of noise than a binary system.
This means that you need higher quality circuitry that can tolerate more electrical ‘noise’ than you do with binary.
When you switch a signal from a zero to a one (or viceversa), you have to wait a while for the voltage to settle. Nothing in electronics happens instantly…but you don’t have to wait for the voltage to climb all the way from 0.0 volts to 3.3 volts before the next piece of circuitry can detect the change. In fact, it’ll know you switched the input from zero to one as soon as the voltage gets over 1.65 volts.
But in a base 3 system, you have a problem. If the voltage climbs up to 0.835 volts (the midpoint between a zero and a one  you can’t tell if it’s going to carry on going up until it represents a ‘two’…so you have to carry on waiting for the voltage to rise until it hits 2.5 volts before you know for sure.
This means that ternary logic is much slower than binary.
Even worse: In a binary system that’s in transition from zero to one  it is always, unambiguously either zero or one. But with a ternary system, as it crosses from ‘zero’ to ‘two’  it will (for a short time) produce a ‘one’. This would be a total disaster in some cases  so instead of letting simple logic elements like ‘AND’ and ‘OR’ gates simply switch logical states as their inputs change  you have to make certain that they never “see” those inbetween states.
This could easily be disasterous  so ternary systems end up with FAR more logic that makes sure that these kinds of things don’t happen.
The final thing is that ternary systems are wasteful if used for everything. For example  the keys on your keyboard are either up or down. We don’t care if they are halfdown. So the interface between your keyboard and the computer is naturally a binary system…using ternary would be a waste.
There ARE situations where ternary would make more sense (can’t think of one right now  but I’m sure there are some). But in those rarer situations, we can use two binary signals to do the job of one ternary one. This is also wasteful  but because it’s much rarer  it’s not as wasteful as ternary would be.
So  all in all, binary beats ternary for MANY things…and quaternary and higher bases are even worse that ternary.