How to calculate the key complexity (in bits) for a combination of 10 characters, each with 100 variations?

Question

Mathematics

You know, there is such a thing - a passphrase? :)

Well, for example, a phrase of 10 words, and in total there are, for example, 100 such words.

How to calculate the complexity in bits (well, you know, there is such a "128-bit key" for example) of such a phrase?

And if there are not 100 but 200 words? And if the phrase is not 10 words, but 20?

Is there some formula for this, understandable to mere mortals? )) Well, can you somehow explain it in human language how to calculate, without all these terrible mathematical squiggles and terms? )) I just want to use it in a real project, and not break my brain))

Thank you in advance.

Answer 1

When talking about the length of the key in N bits, they usually mean that the key can have 2 ^N different values.
Accordingly, in your case, for a phrase of 100 different words with a length of 10 words, we have 100 ¹⁰ options. To express this in bits, you need to take the binary logarithm from it.
You get log ₂ 100 ¹⁰ ≈ 67 bits.

Answer 2

If I understood correctly - please mark it as an answer)) see:
in 1 byte - 8 bits
1 byte - these are 256 variations (say: characters)
i.e. if I have 256 words in my dictionary, then a phrase of 10 such words will be 10 bytes, or 80 bits.
Am I understanding correctly, or am I driving? )))