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What does ULA stand for?
Uncommitted Logic Array.

It was a semi-custom chip type, where the silicon layer was standardised but the metal layers varied by customer.

https://en.wikipedia.org/wiki/Gate_array

Just want to add that they're very common on 1980s computers in Britain. Sinclairs and Amstrads have them. And that they often fail and are very hard to replace. Essentially you end up taking one from another machine, so the stock of working machines declines over time.
Would it be possible to recreate the ULA logic in a modern FPGA? And if so, to use it as a direct replacement in an original Sinclair/Amstrad?
Product name for gate array at Ferrari semiconductor.
Now that is a company that had a wild ride. It could have become the Xilinx instead it ended up with a wild story involving illegal arms exports and other insane stuff.
The ZX81 was a ZX80 with all the 74LS chips boiled down to a ULA (and the "New ROM"), so in a way this is a ZX80 :-)

(I love these kinds of projects.)

Very good point! Didn't the ZX81 add a few things though? It had a CPU based video driver driven by interrupts IIRC so the screen didn't flash all the time when it was working - very, very slow though.
I'm not entirely certain. I know you could upgrade the ZX80 by installing the "New ROM", and I believe that was basically just the ZX81 ROM. Not clear if that gave you everything in a ZX81 such as SLOW MODE (see other replies).
The ZX81 added SLOW mode, which was a big improvement. SLOW mode can be added to the ZX80, which is what was done with the ZX81plus38.
> ... I don't remeber ever having a case of covid, but I do suffer from the same symptoms. I'm 66 now (2021/2022) so I don't see myself getting a job anymore, and consider myself retired.

Really touching to persist with this. Hopefully this work does not all suddenly disappear when mortality takes its inevitable toll.

ZX80/ZX81 were horribly compromised devices, designed to minimise cost based on the components available at the time. I'm not sure why someone would want to emulate one (I could understand replicating one, I guess). Using modern chips, you can build a much more exciting toy for a lot less money.
Because why not? What's wrong with doing a totally pointless hobby?

BTW there's a decent ZX81 FPGA reimplementation in the MiSTER: https://github.com/MiSTer-devel/ZX81_MiSTer

Whilst the purpose might be, the process is great for some learning and for an old man it is great.

If it can simplify might even tell a story, a book etc on how to start from 0 on building your own cpu.

ZX81 was the first computer I ever used. I learnt to code on it. It led me down the path that made me gainfully employed all my adult life. It might have been built to a price point but that price point meant it could be afforded by my family and the rest is history.
Took me a bit of research to figure out that ULA is "Uncommitted Logic Array"
Amazing 66 years old after a long covid (without he remembered getting one). Do not have anything to cheer him up.

Just word: you are amazing.