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Why binary is represented by two bits 0 and 1 and not three bits?
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TheUnnamedNewbie:
There has actually been some revival in multi-level logic recently. With the excess SNR we often see in digital circuits, you could say that you are wasting potential intermediate levels.

Sure, the gates become more complicated, but I don't think that is such a big issue - after all, I think few digital designers still manually do the gates, this is all for the logic synthesis tool to deal with (so you just make the logic synth 'smarter' and nobody has to know about any of this).

I don't think Shannon's theorems provide a big clue - if anything, they really do make you wonder 'why not?'. Just look at the PAM4 digital stuff coming to high-speed interconnects - 112 gigabit/s with very low error rates. And sometimes errors are actually acceptable - think neural nets or signal processing, where there is already a error band on the signal anyways. Does a tiny additional error form an issue here? I've already seen examples of this being used on DFEs in communication systems where you have multi-level data (EG, QAM 16 which has 2 4-level streams) and where using 4-level logic provided very elegant and low-power filtering.

I would not be surprised if multi-level computation is more common-place in the future.

(note - I'm not necessarily talking true analog computation with differentiators and integrators - rather multi-level digital, similar to PAM4 etc)



TheUnnamedNewbie:

--- Quote from: wraper on October 29, 2019, 12:17:14 pm ---
--- Quote from: Raj on October 25, 2019, 09:04:17 am ---They do have additional circuitry next to the storage chip to convert them back into zeros/ones.
--- End quote ---
:palm: ALL SSD have controller chip. And it does not convert anything. NAND flash chip outputs binary data.

--- End quote ---

No need to :palm: here. The converter that goes back to binary could easily be on a separate die within the package - esp given how floating-gate non-volatile storage uses vertical stacking on specialized processes. There is obviously a need to turn your multilevel signal back into a nice digital stream, which has to be somewhere - be it on a special controller or in package or on die.
tggzzz:

--- Quote from: TheUnnamedNewbie on October 29, 2019, 12:23:16 pm ---There has actually been some revival in multi-level logic recently. With the excess SNR we often see in digital circuits, you could say that you are wasting potential intermediate levels.

--- End quote ---

That isn't new; it has been the centrepiece of digital comms systems for over 50 years!

The key is to understand the difference between "baud rate" and "bit rate"; too many people don't.


--- Quote ---I would not be surprised if multi-level computation is more common-place in the future.

--- End quote ---

It will indeed.

With modern and future high speed comms links, multipath effects in on-board and in-cabinet comms links will become problematic. Such comms links will then have to re-use techniques from current "long distance" (i.e. 10m to 100km) comms links. Many of those will be multi-level, to minimise the baud rate.
tooki:
Indeed, a substantial percentage of the digital signaling we use does not rely on encoding a 1 as a high voltage and 0 as a low one. Manchester encoding/NRZ for example is very common.
T3sl4co1l:

--- Quote from: tggzzz on October 29, 2019, 08:06:04 am ---It looks like you are conflating "electric field" with "charge". Analogy: if I have a 1kg weight on a balanced lever, moving the pivot changes the counterbalancing force by less than (or more than) 1kg.

--- End quote ---

Not so much the field as its effect upon materials, which are polarized as a consequence.  Polarization is a displacement of charge, and that displacement is continuous.

Tim
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