If there were 3 voltage levels in a computer, would there be a formula for information?

Question

Informatics

The textbook has the formula D = log2(logarithm power)N bits, where D is the amount of information, N is the number of different states. I didn’t understand at all where the degree of 2 of the logarithm came from, through the search engine I found proof through entropy that in order for a sign to become information, it is necessary to ask it a question, the answer to which will give 1 bit of information, and the question itself will have two conclusions: yes and no . But if we had 3 states, then the formulawith 1 sign, it would give out 2 bits (we round up, because in order to encode 3 states with two values, at least 2 bits are needed: 00, 01, 10), although in fact our question already contains not two answers, but three, thus with records of one character, we must also receive 1 bit of information. Isn't this formula currently a special case for representing information through a binary system, when, as on the Internet, it is presented as a general information formula?
https://medium.com/nuances-of-programming/introduction...

Answer 1

Everything here is tied to the fact that a bit is 2 states. Therefore, the logarithm is binary. If a bit had 3 states, then it would not be 2 binary bits - you can’t round like that (let’s round your rent up to 100,000, are you okay?). The logarithms would be base 3, because each new tribit would multiply the number of possible states by 3.

Answer 2

This formula, as a measure, does not imply a specific value, but describes its order / degree for evaluating dependence,

the same situation with labor intensity

, вас не сильно волнует (пока до конкретики не дойдешь) какая константа N у формулы N*x*log(x), вас волнует только X*log(x) ибо точно описывает на сколько алгоритм сложный

So the logarithm has the property that the logarithm of any degree can be reduced to the logarithm of any other degree by multiplying by a constant because logA(b)=logC(b)/logC(A), i.e. if you have base 3 then log3(b)=log2(b)/log2(3) ~ 0.6309*log2(b) , the constant is removed from consideration and it all comes down to the same double power logarithm
. when moving from 2 to 3 bits, the amount of information will change to a constant, and not to a power, which means it is insignificant and can be excluded from consideration