Bits and digits are particular cases of what?

Question

• A bit is a _____(1) that can take two different values: usually 0 or 1.
• A digit is a _____(1) that can take ten different values: 0, 1, ..., 10
• A _____ (2) is a _____(1) that can take 16 different values: 0, 1, ..., 10, A, ..., F.

Questions: A: Is guarism the right word for (1)? B: What would (2) be? In other words, what is the name for an hexadecimal (1)? C: What is the number of different values a (1) can take called?

Answer 1

As far as I can determine, guarismo is a Spanish word that can mean either numeral or digit (in the sense of a numeric digit).

There is no English word guarism, and (as far as I know) there is no English cognate for guarismo that would be suitable here. (Algorithm has been suggested, but it does not fit in this context.)

To fill in the blanks that are written "______(1)" in the question, I think the correct word is digit. There are also less specific words, such as symbol, but digit seems to be a better choice: it is one of the most specific terms that fits in the blank.

The second sentence should read,

A decimal digit is a digit that can take on ten different values: $0, 1, 2, \ldots, 9.$

We say decimal digit in this context precisely because the word digit can occur in the context of any place-value system. Even the word bit in the binary number system is derived from the words binary digit.

For base sixteen, we use hexadecimal digits or base-sixteen digits.

Answer 2

I have never heard anything other than "hex(adecimal) digit" for your (2).

I am not sure there is any word for what you ask about for (1) -- or indeed what the precise semantics of the word you're looking for is. The closest word in common use is probably "digit" itself.

I have never heard "guarism", and Google finds no evidence that it's used with a meaning even close to what you describe.