Any expression can be represented with only NANDs
IDEngineer has given the first half of the answer. The second is: the Boolean algebra with related concepts. While the Boolean algebra was not getting much attention before second quarter of 20th century, it was quickly recognized as a perfect tool for the job. It is deeply connected with prepositional logic, finds its place in multiple branches of mathematics, uses a tiny number of elements in implementation(1), allows super easy synthesis of circuits.(2)(3) and everyone knew how to prove the circuits to be right.
Trivia: there also were negabinary computers. Anecdotal story is that the guys misunderstood a joke and implemented the machine, approaching the subject with complete seriousness.
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(1) Any expression can be represented with only NANDs or only NORs, in the past also only a set of AND/OR/NOT gates. Each of those are trivial and robust circuits.
(2) E.g. De Morgan’s law quickly turns any messy expression into simple, conventional form of OR-of-ANDs or AND-of-ORs, which is a circuit consisting of at most 3 layers of digital gates (optional NOTs, a bunch of ANDs, a single multi-input OR).
(3) Historically Karnaugh maps have been used, and those can be solved by children in kindergarten.
Btw cheap Solid state hard drives do store more than just on/off or 0/1 per cell, they are like 0/1/2/3 per cell.
They do have additional circuitry next to the storage chip to convert them back into zeros/ones.
They do have additional circuitry next to the storage chip to convert them back into zeros/ones.ALL SSD have controller chip. And it does not convert anything. NAND flash chip outputs binary data.
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.
I would not be surprised if multi-level computation is more common-place in the future.
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.
In uni we were given an assignment to build a logic circuit to run a 7 segment display from a 4 bit binary bus input. We were only allowed to use NAND gates. Was quite challenging and quite interesting to do. Think it ended up being about 50 gates.
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.
There has actually been some revival in multi-level logic recently. [...] Sure, the gates become more complicated, but I don't think that is such a big issue
So, I would claim that it is precisely the complexity that is the issue.
CMOS consumes barely any current when staying in stable state, current flow happens only during changing state.
CMOS consumes barely any current when staying in stable state, current flow happens only during changing state.
No longer true in the latest semiconductor processes. Reducing static leakage currents is a hot topic.
CMOS consumes barely any current when staying in stable state, current flow happens only during changing state.
No longer true in the latest semiconductor processes. Reducing static leakage currents is a hot topic.There is always some leakage. But calling it "no longer true" is nonsense. That leakage is somewhere in femto-picoamps range per single transistor.
Trying thinking how you would create any sort of logic gate or arithmetic circuit that isn't based on binary. There's not a benefit to doing so.
Then multiply that by the number of transistors
The figures I've seen are that the leakage power dissipation can be 30% of the total power dissipation. That will, of course, be dependent on the specific process.
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.
I think Manchester/NRZ was not what we were pointing to, it still uses only two levels. Rather things like PAM4/6/8, BPOOK, multi-level ASK/FSK etc...