How does LOGIC work internally?

The LOGIC module is a bare digital, boolean logic module, your example of AND is correct. You can use it for audio; I personally prefer the XOR (exclusive or) for very gritty stuff.
But yes, it's not a ring modulator which works analog / with analog values.

You can create a logic OR with the LOGIC module by using so-called NAND-Logic; Wikipedia has a good explanation: en.wikipedia.org/wiki/NAND_logic
What you do is inverting both signals by using IN3 / IN4, feed INV3 / INV4 into the inputs 1A and 1B; the output NAND 1 gives you the OR then.  ...boolean logic is amazing, isn't it? Basically, with NAND gates, you can build EVERYTHING digital, even a complex processor! Same goes for NOR gates; e.g. the Apollo guidance computer that controlled Apollo 11 at the moon landing was built entirely with NOR gates (with 3 inputs each, and 4100 of them) and ran real programs stored in a ROM memory. See en.wikipedia.org/wiki/Apollo_Guidance_Computer

I’m sure the inverter on the ATT module does not round i.e. It does invert the signal, That’s why it can be used for side chaining and subtracting voltages.

Lacking an oscilloscope I can't verify precisely. But on my logic module, if I route a sawtooth wave into the inverter, and then take the result out to CV a filter, it sounds very much like the filter bounces back and forth between two positions. But if I put the saw directly into the filter, the result is smooth interpolation.

From this I figured that the inverter takes any value X between 0 and 5v, but instead of changing it to 5-X, it changes it to ROUND(5-X), where Round(u) is 0 if u < 2.5, else 5. It looks like AND does as well. This would make sense for digital logic but is unfortunate for analog. You're saying that this is not the case? I would like to be wrong!

Thanks. I just did another verification. NAND, AND, XOR, and INV are all rounding on the LOGIC module -- that is, their outputs are always fixed high or low (probably 0 or 5v). So perhaps INV would be better called NOT. Useful for certain cases but not in my situation: I gotta go get an attenuverter!

I suppose that it depends on your experience, but I never considered the LOGIC blocks as anything other than digital, Boolean logic — inverter is a common term when describing such gates (even though some implementations like the CD4069 actually have a small linear region!)

Interesting to consider the binary operation as ‘rounding’ too; I’m wondering whether this train of thought might be interesting in some cases 🤔🤔🤔

I never considered it as rounding either, I supposed there was just a bunch of CMOS CD40xx chips in there for the different operations, so I only supposed there might have been some hysteresis involved?

Still got to experiment with the CD4069 further.. I've got a bunch of them on the breadboard and tons of circuits online which use it to do filters, weird VCA's, even someone who made a 'big muff' fuzz pedal with almost exclusively CD's! Crazy chip.

Wait, I can get ring modulator-like results with NAND?

Since AM (amplitude modulation) was mentioned, this can actually be done with a VCA, by putting another audio signal in the CV in, right?
I guess this is quite close to ring mod.

I find bitcrushing is another that generates results in a similar ballpark at less crazy settings. Maybe worth mentioning you can do that with an S&H at audio rates.

I've had several of the K's - the k1 which has a really lively digital sound, albeit without filters unfortunately, the k3m which was lovely - really nice SSM filters but limited in terms of range of parameters (0-31 was it?! Who knows why) - and the k5m which somehow managed to do bass pads due to its thinness, aliasing and additive engine - I used to love sending it really low chords and hearing it unfold.