TLDR
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Intro
I know the analog computer was actually invented long ago. I don't know how analog computer architecture was, but I guess it was using active components.
As a computer engineering student that study both electrical engineering and computer science, we are taught to map the physical value to the logical value, regardless of the physical instrument being used. This major basically gives an interface to the computer science major about what they want to apply to their theories.
There are many physical instruments that have been used to perform computation. For example, in mechanical engineering such as gear and levers that depend on Newton laws (this is the computer engineering major's grandfather), electrical engineering components that depend on Kirchhoff laws, and recently being in research is quantum computing that applies Max Planck theory.
But the most popular and still being used today are electrical components.
The main physical value that is being used is voltage. That's the most digital computer nowadays being used. It mapped VCC to logical value 1 and GND to logical value 0, (depends on device logic convention). But no matter how it mapped, that's a binary digit.
This is the reason why computers nowadays are called digital is because they work on many digital values, specifically binary digits (bits).
Question
Now, instead of discrete-binary mapping, I want to map the physical value of voltage to any range of real numbers.
For example, -1V to 1V (physical value) will be mapped to the real number -200 to 200 (logical value).
Now let's talk about basic arithmetic operation. I do realize that it's impossible to perform any gain or amplify or incremental operations with just using passive components only. So, I will try exploit decremental operations.
So far, I found decremental operation that suits for arithmetic operation specifically addition operation. It's voltage divider as addition operation.
VOUT = (VIN_A + VIN_B)/2
Given physical value limitation of -1V to 1V with logical value map -64 to 64.
LOGICAL_VALUE_OF_INPUT = VIN * 64
LOGICAL_VALUE_OF_OUTPUT = VOUT * 2
It multiplied by 2 since there is divisor factor on voltage divider which is divided by 2.
Now, I'm wondering how to perform logical multiplication operation with exploiting decremental physical operations on RLC or any passive components?
For flexibility, you can use any physical values like current, load, resistance, frequency, etc. to represent logical value, so this question is not limited to voltage only.
Why am I asking this?
If you are asking why I asked this ancient question, it's because I'm wondering if it's possible to implement an AI accelerator on analog since analog is noisy and most AI, deep learning, or machine learning is tolerable with inexact value. Thus, it suits with analog technology instead of GPU power hungry. Moreover analog computing is faster, assume we exclude logical-physical value conversion time.