Bit depth becomes continious, essentially. Instead of a 32 bit number, you just have any number you please, as it's continuous. Granted, there are restrictions in translating this to memristors, but thats essentially the gist.

The real key feature of memristors is not the math or any of that stuff, it's that all that math is stable under power cycling and it take nearly no power to compute things. The article mentions that they preformed 188 GigaFlops with about 0.3W of power. The human brain is about 20W at about 1 ExaFlop (a VERY coarse estimate) for comparison.

This power savings opens up the doors for very good computation (ML stuff) on very tiny power sources.

How’s that “bit depth” different from the bit debth you get when you implement a simple analog summing circuit?

The number of elements required is much less.

The 'standard' summing circuit [0] typically requires an op-amp, which is in itself a multi-element component, and a few resistors. With a memristor, you can theoretically skip the op-amp and just use the passive elements, though an op-amp is likely still needed to read out the very small signals [1].

[0] there are MANY ways to skin this cat, but here is a simple one: https://www.electronics-tutorials.ws/wp-content/uploads/2013...

[1] https://image.slidesharecdn.com/1205-141021211518-conversion...

The opamp is mainly needed of impedence matching. There are several ways to contruct such circuits using just inverters.

Analog computers in the past were mostly used to solve differential equations. The input was voltage levels. You could add, multiply, integrate or combine multiple inputs. The is what is done in artificial neural networks if you imagine the voltage levels as input.

https://en.wikipedia.org/wiki/Analog_computer has many examples. For example, mechanical computers used to be used for fire control on naval vessels: https://www.youtube.com/watch?v=gwf5mAlI7Ug

Very easily. Analog computation used to be very common.

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

Analog computers predate digital ones. Technically even slide-rules are computers!