I think the idea is that you use registers and apply the NOR gate multiple times. In this sense the NOR gate is universal, while an OR gate nor a XOR gate are neither universal.

I.e.

  XOR(x,y) = NOR(0, NOR(NOR(x,y), NOR(NOR(x,0),NOR(y,0)))))

(maybe not the most minimal version and maybe even wrong)

Fun logic tongue twister: Neither an or gate nor an xor gate are universal

Any expression or series of gates of only ORs has the non-decreasing property, changing an input from 0 to 1 can never change the result from 1 to 0. So you can't implement any gate that needs that using ORs.

Similarly, any collection of XOR gates is simply a summation mod 2.

From the website: http://www.mynor.org/downloads/NOR-Logic.pdf

Thanks but in the linked PDF they use 12 NOR gates for a ONE bit adder.

Then you need at most 12 registers for a one-bit adder.

The nor gate (like nand) is a universal gate. You can implement all the other gate with a combination of nor gate. See https://en.m.wikipedia.org/wiki/NOR_logic#XOR for example.

Not with a 'single NOR gate'.

Yes .. if you feed its output to its input on the next cycle.

Then the ALU includes the sequencer and the microprogram.

Shifts are implemented with look-up tables.

Anyway it's a beautiful work.

NOR (like NAND) is a universal logic gate. You can build any other logic gate out of just NORs.

For this ALU, you’d presumably write a subroutine that computed XORs in terms of NORs, and then use that as a primitive for building an adder.

Yes, but this thing advertises that it uses a single NOR gate as an ALU.

That’s just moving the composition between hardware and software - the equivalence still applies. I can build any logic (software) function out of a function that evaluates NOR.

False advertising, then, IMO.

No, AFAIU the computation is serialized, driven by the microcode and this gate is reused for every step

...but that's exactly the claim, restated.

Not really. It's completely trivial, if extremely slow (which the article acknowledges) to emulate an ALU in software, with access to a single, universal hardware gate. Why don't they just say "we put a NOR gate on a chip, then added all this other stuff (RAM, boot EEPROM, etc.) to make it function as a computer." That would, at least, be a non-misleading statement of the claim.

Yes, it's a "Single board computer with 20 ICs, and a single-gate ALU".

To me it's not really an ALU either, since the NOR gate doesn't really do the job I expect from an ALU.

That’s how I interpreted the OP though... I really don’t know what you were reading into it.

http://www.mynor.org/downloads/MyNOR-HowItWorks.pdf has some more info.