[tromp]

It's binary with the central dot/ding being the leading 1 and then toward the right

a ring is 0

a ring,ding is 1

The ring represents a doubling of its contents. The special case for the leading bit could be avoided by always having an innermost empty ring. That would also give you a better (i.e. visible) representation for 0. The addition rule ensures that you always have exactly 1 leading 0.

[whatshisface]

It's not binary because all of the intermediate results shown during the videos are also valid numbers. It's actually an (upside down so as not to spoil it for anyone) ˙ǝuo ɟo uoıʇıppɐ ʇuǝsǝɹdǝɹ sʇop ǝɥʇ puɐ 'oʍʇ ʎq pǝıןdıʇןnɯ sʇuǝʇuoɔ ǝɥʇ ɥʇıʍ sısǝɥʇuǝɹɐd ʇuǝsǝɹdǝɹ sǝןɔɹıɔ ǝɹǝɥʍ uoıssǝɹdxǝ ɔıʇǝɯɥʇıɹ∀

[taejo]

From the article:

> The rings must be nested. The innermost ring must have a ding. No region can have more than one ding. Those are the only rules.

According to these rules the intermediate results are not valid numbers