I have actually been needing something rather similar for ages now.

You see, I have always needed the ability to run more complex mathematical computations in-game like square roots, sine, cosine, etc(this is related I promise). Unfortunately, the most the game provides is addition, subtraction, multiplication, division, and modulo operations(see here). To make things worse, I am not allowed to work with any number that isn't a 32-bit integer as scoreboards are restricted to work with those. This makes it much more difficult to work with almost any kind of rational/irrational numbers, as well as really big/small numbers.

So I set out to develop my own solutions. I started with trying to get a square root algorithm working in game, and I succeeded. However there was a problem. It could correctly compute roots for perfect squares/cubes/etc, but it gave incorrect results when dealing with imperfect squares/cubes/etc. Now I believe I used the Babylonian method for computation, and from what I could tell, what I wrote should have worked. This was up until I noticed that when the game does division, it rounds the output down to an integer. This meant that every time I ran my square root algorithm, it was rounding stuff it shouldn't have been rounding, and thus gave an incorrect result.

Irritated, I decided to drop the project for a while. I later came back and decided I was doing this all wrong. I needed to ditch Minecrafts way of doing it and start from scratch. So I started developing my own binary system inside of a datapack, and am currently planning to work my way back up to more advanced calculations.

So far, I unfortunately haven't made much progress, although I have made some. I am currently using the scoreboard and a bunch of marker entities to store each binary number into a bunch of bytes. From here, I can bit shift my numbers left/right, and can add them together. In theory, this system can work with numbers up to 2^(8*(2^31-1)), or 2^17179869176 to be more precise. There's no way the game is going to be able to work with a number like that with how massive it is, but it's still fun to think that it could in theory if given enough time/resources. :)

The way I got the above number is simple: I am dividing our binary number into groups of 8 bits, and storing them into their own markers(AKA: each marker represents a byte). Each marker/byte is also given a score from 1, up to 2^31-1 to distinguish the byte from the rest, depending on how many bytes we need(8 * (2^31-1)). From here, I just take 2, and raise it to the power I just calculated for our total number: 2^(8*(2^31-1)).

Currently I am trying to figure out how to simplify the code as it's a mess. I'm also trying to make it capable of displaying numbers as a float/decimal/integer/etc. No idea what approach I'm going to take yet, or if I even should go for a float as it might be more performance hungry.

All of that aside, if you wanted to load a binary number from a .mcfunction file, you could do that. Could be as simple as setting all of the bytes in the .mcfunction file for each number, then bit shifting in game to read the number. :)

If you want to give the datapack a try, let me know and I can give a download link. Please understand though that this is far from complete, is very messy, and likely full of bugs.

I am not sure what you mean. Redstone is just a bunch of blocks placed in the same area to create mechanics. Can you give an example of a simple redstone machine and how do you want it to be translated? And what exactly do you need it for? Perhaps there is an alternate solution.