Nibbler 4 Bit CPU (2013)

It's worth noting that 4-bit microcontrollers are still in widespread use in ultra-low cost high-volume applications, where they use mask ROM and are usually in the form of a COB mount. Remote controls, 4-function calculators, and https://en.wikipedia.org/wiki/Handheld_electronic_game are some examples of where they can be found.

Has anyone ever written a BASIC for a 4-bit CPU?

Well, he uses a '181 ALU chip -- which is very nice but you have to scour the universe to find vintage logic parts like that any more. Amusingly, it is easier to find vintage vacuum tubes than vintage TTL logic. For that matter... you can find Youtubers building vacuum tubes from scratch using crude home shop tools, which don't quite cut it for TTL logic.

For something you could build with today's part catalog, without going all the way to an FPGA, doing the ALU in a GAL parts might be both amusing and educational.

A couple of years ago I have built a copy of this project with my son on a breadboard with real (made in '80s and '90s) 74-series chips.

It was a very fun experience. And we liked the project very much.

It has a very small and concise schematics which makes it very easy and clear how CPU really works.

P.S.: the original simulator is written in C++/CLI (a .net flavour of c++), so I decided to refresh the project (to c#, it was easier to translate than to port to native c++), and added a real 1602-display simulator which looks nicer and support a “graphic” mode. You can play with it here https://github.com/omgtehlion/nibbler-sim

but also

https://futurama.fandom.com/wiki/Lord_Nibbler