[tgot]

I think that your description is almost excellent, but that you're fundamentally misleading in describing what you are doing as a "30-bit" digit.

It's a 10^9 digit mathematically, occupying 30 bits of storage. You do briefly mention that it's 10^9, but repeatedly say 30-bits.

[samatman]

It isn't misleading at all.

A hexadecimal digit has 4 bits of entropy. You can guess it correctly by chance one in sixteen times. Calling that a four-bit digit is correct. Same with a 30 bit digit, all that changes is the magnitude.

The "storage bits" aren't a detail, they're an essential property. Stored in balanced ternary it would still have 30 bits of entropy.

[derdi]

I think you misunderstood the parent. If you speak of a number in the range 0-15 stored in 4 bits, we can all agree that "4 bit digit" is the appropriate term for it. But what about a number also stored in 4 bits but restricted to the range 0-13? It's a digit that fits in 4 bits, but calling it a "4 bit digit" without further qualification would omit relevant information.

[samatman]

That hadn't occurred to me, I had thought (having read the Fine Article, but not closely, nor really more than glanced at the code) that it was using exactly 30 bits and reserving two for, IDK, carry detection, and that 10^9 was just approximating 1073741824. We do that every time we call 1024 a KB and not a KiB, so there's precedent.

Ok. Fair. It's a ~28.9 bit digit taking up 32 bits of storage. It turns out I was mislead!