the largest number representable in 1 bit is any number (including +infinity and beyond).
This article describing various Rube Goldberg machines, there is no need to agree on different ways of representing numbers when one can set a single bit to 1 to represent any desired pre-defined number, or 0 to represent its absence (or the number 0).
Programs like Melo and w128 are the opposite, performing a hard task with the simplest means, using only a few highly inter-related parts.
Your proposed representation is exactly the kind of cheating, to get the results you want, that the article purposely avoids.
2. Using a Turing machine to model a von Neumann machine looks exactly like a Rube Goldberg machine. It even resembles it [1].
3. There is no point in talking about a 64-bit limit when the underlying model requires an infinite amount of RAM (tape).
4. > A Rube Goldberg machine is one intentionally designed to perform a simple task in a comically overcomplicated way
People usually don't realize they've built a Rube Goldberg machine...
5. > Programs like Melo and w128
My point is that just as you pre-defined the program you're going to use, you can pre-define the largest integer. That's 1 bit of entropy. I was working on a project with custom 5-bit floating-point numbers implemented in hardware, and they had pre-defined parts of the mantissa. So the actual bits are just part of the information.
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1. https://en.wikipedia.org/wiki/Turing_machine#/media/File:Tur...
