[asimpletune]

It's called radix economy. Different radices have different efficiencies as defined by the ratio of number of digits in a radix alphabet over the number of placeholders required.

Simple example, base 1 is obviously inefficient once counting past 1. Similarly base 1 million is inefficient (until you're counting in the bazillions)

[scotty79]

If you can store one digit of a number base million in one physical element then it's exactly as efficient when it comes to storage of digits as binary. One element per one digit.

But it's about 20 times more efficient when it comes to storage of whole numbers because you can store number up to a million in a single physical elements while binary needs 20 elements.

[asimpletune]

I see what you're trying to say, like I understand the intuition, but like I was saying earlier this is an already understood topic https://en.wikipedia.org/wiki/Radix_economy and that point has been addressed. Sorry, not trying to be a jerk. Just wanted to point that out in case you're interested in this subject.

In the example you gave, I'm assuming by 'physical element' you mean 'placeholder' or digit. Storing more numbers in a single placeholder seems like you're just getting efficiency for free, but that's not how information works. You have to come up with a unique symbol for one million numbers (0 - 999,999). Which you have to pay for.

base 64 is a more realistic example. With 64 characters per digit, it may seem like it's more efficient, since you require less digits to express the same number as base 10 or 2, but you still have to encode 64 unique characters, and it ends up being less efficient. That doesn't mean less efficient is worse. It just means it is more specialized and used for different things. For example, base64 gets used when you want to encode information in a small amount of space. Otherwise, for the actual storage and computation of data, lower bases are preferred, and base 64 is still obviously stored as binary.

For what it's worth, the base integer with the best radix economy is 3, followed by 2.

[scotty79]

Thanks. I should have googled this when you mentioned it.

I see that radix economy makes some sense if you assume that the "cost" of the "element" is not fixed but linearly proportional to the number of different states it needs to hold. It was apparently linear for the computers built with triodes but log2(n) to hold n states seems more realistic in electronics. Maybe little more for error resiliency.