A 1-bit CPU?

(the project above is just a quick sketch/prototype of what I'm thinking of. it's kind of documented in the comments. also, the reason why everything is just "lb 0" after some point is because 0x00 is interpreted as that and the memory is just initialized to all 0s)

So recently I've been thinking about if it would be possible to make a 1-bit CPU. The major problem with this is that you can only address 2 locations in memory, 0 and 1. It seems like a lot of 1-bit processors that were actually sold used a separate register for addresses (question: does it still count as 1-bit then?). I've implemented a (very bad, and probably very buggy because I didn't test anything beyond the sample program which is 3 instructions) prototype of something like that in the project that I've linked. Something else that I thought of would be to have separate registers that are put together to make a single register with more bits, but at that point it would probably just not be a 1-bit CPU. So is it possible to make a "true" 1-bit CPU that can actually do things beyond 2 bytes of memory?

In a 1-bit-wide computer, it doesn't make sense to talk about memory in bytes.

But a Turing machine is a 1-bit computer. Look up how they're programmed and, in particular, how they address memory (the tape).

Hi there! I find the idea of a 1-bit CPU fascinating and I'd love to learn more about it. Your project seems like a really cool way to explore the fundamentals of computer architecture in a simplified way.

I have some questions about your project. How does the 1-bit CPU work? How do you program it? What kind of applications can it be used for?

I am really interested in learning more about this project, and I'm looking forward to hearing back from you!

Haven't been checking this forum recently, apologies for the late response.
It basically has some 1 bit registers and some 16 bit ones for the addresses and some instructions for operating on them. There should be some rudimentary documentation in the source code.
Right now there's no I/O apart from the memory and register displays but you can probably memory map something easily