She puts a 0-marble through B to reset the state of the machine, and then, at last, picks up a single 1-marble, and puts it into A.

It falls down and tips over the basket as previous marbles have, retracting the B-input platform. This time, though, it is heavy enough to tip the counterweighted rail, and so it rolls the other way, into a different holding basket.

She puts a 0-marble into B and watches what happens.

It falls down, past the retracted platform and un-moved paddle, and hits a counterweighted rail of its own. It is too light to budge the rail, so it rolls one way and makes its way out of the "A+B 2's digit" output. On the way, it hits a lever which tips the 1-marble out of its basket and out of the "A+B 1's digit" output. 

Then, if she puts them in the other way around, a 0-marble into A and a 1-marble into B?

The 0-marble flips the B-paddle into its intercept position, and falls out of the "A+B 2's digit" output. The 1-marble gets shunted over by the paddle and comes out of the "A+B 1's digit" output.

Hmm.

She gets another 1-marble, and tries putting a 1-marble into A and a 1-marble into B.

This time, the A marble rolls down the counterweighted rail and into its waiting basket. The B marble falls past the paddle and onto its own weighted rail, where it rolls the other direction. It hits a lever that tips the A marble the other way out of its basket, into a tube where it releases a 0-marble from the internal reservoir and out the "A+B 1's digit" output. The A marble then drops out of the "extra marbles" output and the B marble makes its way to the "A+B 2's digit" output.

Hmm!

...she looks for a way to replace the 0-marble in the internal reservoir.

There's an opening on the back that feeds into the reservoir. It holds about ten 0-marbles at a time.

She puts one back in to make up for the one that was spent.

She stands there, a marble in her hands, gazing contemplatively into the machine.

She methodically repeats all the basic addition operations: 0+0, 0+1, 1+0, 1+1. (And replaces the spent 0-marble again.)

Then she... stands there, gazing thoughtfully at the machine.

Sandalwood is content to leave her to her thoughts, although she does also summon a whiteboard on which she writes down the results for easy reference.

"...can I see... what it looks like... when you put them together to add more numbers?" she asks hesitantly.

"Sure," Sandalwood agrees. She creates a freestanding wall of half-adders, with their inputs and outputs hooked together to make a full 5-bit adder.

"Give me two numbers between 0 and 32," she requests.

"...um, um... two? And three?"

"Alright," Sandalwood agrees. This version has a little rack that you can set up the marbles in, and then a lever to pull to release them all at once, because you can sneak in quick changes when you have a self-tree that's very excited about first contact to help. The half-adders still have the basket mechanism and you can reach past the rack to put marbles into the inputs directly, though, because that makes it more explorable.

She fills both racks with 0-marbles, except for the first two places. In the A input, she puts a 1-marble in the 2's position. In the B input, she puts a 1-marble in the 2's position and the 1's position.

"3 is one 2 and one 1 in the encoding the machine uses," she remarks. "Go ahead and pull the lever and see what happens."

...she pulls the lever.

The marbles cascade through the machine, spitting "000101" out of the output tubes and an extra '1' out of the 'extra marbles' output.

"That's one four and one one, which is a total of five," Sandalwood supplies. "Go ahead and try whatever you'd like now -- I just wanted to show you an example of how the input and output are encoded, because that's one thing about this kind of machine that people sometimes have trouble with."

Hmm, so...

First she tries to find just the last part, the part that should be the same as the other machine, and verifies that it still does 0+0, 0+1, 1+0, and 1+1 just the same. (And that it still needs her to put a 0-marble back in after adding 1+1.)

This remains true. The individual half-adders are clearly separated from each other to make it easy to tell them apart, and they are all identical both to each other and to the existing model which she examined before.

Okay!

She moves over to the next half-adder and tries to verify it the same way.

It is an identical device, and behaves in the same way, except that one of the outputs (the 1's digit) feeds into the A input of the first half-adder she examined. The 2's digit output is labeled 'carry' and goes through a little basket-lock system that is also connected to the 2's digit output of the first adder. With the state of the first adder as it is right now, the basket dumps 0-marbles out the back and onto the 'extra marbles' ramp.

Sandalwood vaguely wonders whether she's going to try and validate all 10 of the half-adders. She decides that it's note of her buisness, and blinks open her messages to catch up a little, while keeping an eye on their visitor.

No, the next thing she does is try to operate the two adjacent adders together. By putting in... it looks like three zeroes is what this arrangement expects?

If she plays around with the three inputs of the two half-adders (since one input of one is connected to an output of the other), she can get them to produce 00, 01, 10, or 11 as outputs, with the extra marble dumped out the back.

Before trying anything involving a 1, she goes back and forth a few times between putting in two zeroes to the last half-adder and three zeroes to the assembly of both of them, trying to get a sense for how the two machines interrelate.