Analog Computers: Digital vs. Theoretical Possibilities

[Svein]

Analog, digital and voltmeters...

Let's see. A 12 bit ADC (analog-to-digital converter) is relatively inexpensive. So the output (12 bit) should be within 1 bit. 1 bit in 12bit equals 1/4096 or 0.024%.

How do you produce an analog front-end with 0.024% accuracy?

And - worse - how do you keep that accuracy over the wanted temperature range?

Sadly, people tend to trust every digital bit even if the low-order bits are pure nonsense.

Once upon a time - some customers wanted us to measure the pressure in the fuel lines of a jet engine. In order to have a precise measurement, they wanted a 16 bit ADC. 1 bit in 16bit equals 1/65536 or about 16ppm. Even if we could measure pressure that accurate, what with the noise and vibration from the jet engine at >100dB? The customer is always right, so they got their 16bit ADCs - and a hefty digital filter backend to remove the noise.

 

[jim hardy]

@ is not working again

@ISamson
As recently as the 1960's digital computers were just too slow to solve differential equations quickly.
I worked in a factory that made computers for Cape Canaveral, they were hybrids.
A digital computer set the adjustable resistors in an analog computer that solved the equations and read the answers at desired times.
The adjustable resistors were plain old multiturn potentiometers turned by tiny motors under control of the digital computer.

If there are any left today they're relics.
https://archive.org/stream/TNM_Milg...ter_System_-_Milgo_Ele_20171110_0135_djvu.txt

oh my goodness here's a picture of the assembly line !
https://www.floridamemory.com/items/show/38724
this should take care of the copyright

Milgo Electronic Corp. technicians working on computer production line - Miami, Florida. 196-?. Black & white photoprint, 8 x 10 in. State Archives of Florida, Florida Memory. <https://www.floridamemory.com/items/show/38724>, accessed 11 January 2018.

 

[Phillip81]

I like this. I have always wondered 1 important aspect of computing, what is analog?
Everyone assumes an analog computer is mechanical in nature. What if it was PWM instead. so use 0-1023 instead of 0 and 1. my poor little brain has no idea about transistor and the like but with about 100 arduino nano's taking a read and writing to the next you could make a baby analog for just on $200 (if you buy the el cheapo).
theoretically I believe that you could make a program that needs less junctions to get the end result. so 1 +1 in binary is 8 bits + 8 bits. in analog it could be 1 digit plus 1 digit. The only Issue I foresee in my way of doing it is that you go analog to ditital to analog to digital... over and over and over again.

 

[Rive]

I have always wondered 1 important aspect of computing, what is analog? ... What if it was PWM instead. so use 0-1023 instead of 0 and 1..

Binary logic is just the most common and practical variation of 'digital', it is not absolute. In theory, there is no issue with - for example - ten state logic.
This way what makes the difference between analog and digital is not the amount or value of signal levels, but the way of computing. If you (your equipment) does the computing digit by digit logic, with keeping the logic levels discrete then it's still digital.

theoretically I believe that you could make a program that needs less junctions to get the end result.

In theory, you are right... But the practical part is totally different. To make a not-binary digital system is quite a challenge.

Ps.: well, I mean it's a challenge if you want to make it in electronics. The classic pen-and-paper calculation method is a good example for non-binary digital 'system'.

Ps2.: since at young age it takes some years to master it, maybe we can still recognize it as a challenge

 

[Asymptotic]

As recently as the 1960's digital computers were just too slow to solve differential equations quickly.
I worked in a factory that made computers for Cape Canaveral, they were hybrids.

What was old is new again :)
"Not Your Father's Analog Computer". From the article,

The analog processing on a computer of the type my colleagues and I have developed typically takes about a millisecond. The solution of differential equations that involve only one derivative typically requires less than 0.1 microjoules of energy on our computer. And it takes one half of a square millimeter of chip area if we use plain-vanilla fabrication technology (65-nm CMOS). Equations that involve two derivatives take twice as much energy and area, and so forth; yet the solution time remains the same.
...
With a 300-millimeter wafer, this would permit more than 100,000 integrators to be placed on the chip, thus allowing it to simulate a system of 100,000 coupled first-order nonlinear dynamical equations, or 50,000 second-order ones, and so forth. This might be useful, for example, in simulating the dynamics of a large array of molecules. The solution time would still be in the milliseconds, and the power dissipation in the tens of watts.

 

[FactChecker]

The F-16, F-111, and several other fighters had analog computers for their flight controls till the mid 80's. It was easier to design their response to the dynamic frequencies of the airplane. As long as the logic switching remained relatively simple (compared to modern flight controls), analog computers worked well. There is a trade-off between analog and digital computers. Analog computers have no trouble responding to very fast frequencies but have trouble with complicated logic. Digital computers can handle incredibly complicated logic, but may not do it fast enough for high frequency responses. Modern fighter flight controls can be incredibly complicated and push the fastest digital processors to their limits.

 

[Babadag]

In my opinion, the word “analogue”, like many words in English - meant something else initially. Now any device that is not digital is considered analog-even mechanical one. The analogue word was used for circuits that could mimic arithmetical operations as sum, difference, division, and even integral. See https://en.wikipedia.org/wiki/Operational_amplifier
So it was once upon a time an analog computer. However, there were mechanical computers also [see for instance “Enigma” German product in WWII].
https://en.wikipedia.org/wiki/Enigma_machine

 

[Baluncore]

A GPU with over a thousand processors, each running at better than 1 GHz, is capable of emulating a few hundred analogue computers in real time. If you don't believe it, design your analogue computer, model it with SPICE, and run it on a PC.

I have yet to find a true digital gate used in a digital computer. Every logic gate is a circuit made from transistors, resistors, diodes and wires. The circuits implement an analogue of the boolean logic functions.

Consider two voltages, A and B, each varying between 0 and 1 volt, each representing the probability of that particular input being true. An AND gate can then be a simple multiplier. The output voltage, Z, will be the probability of both inputs being true. Z=A*B. If both inputs had a probability of 0.5V then the output would be 0.25V which makes statistical sense. An inverter would be made from a subtractor, Z=1–A. Then the NAND gate becomes Z=1– A*B. The set of basic functions becomes;
NOT(A) = 1–A
AND(A,B) = A*B
NAND(A,B) = 1– A*B
NOR(A,B) = (1–A)*(1–B)
OR(A,B) = 1 – ( (1–A)*(1–B) )
XOR(A,B) = B*(1–A) + A*(1–B)
Not one of those is a digital gate, yet if you are certain of the inputs, they all perform boolean logic.