It's been posted before: http://www.bzarg.com/p/how-to-pronounce-hexadecimal/

F-hundred and c-tee-five doesn't just roll off the tongue does it?

I think it would be better to just use new words. Using decimal digits for another base gets a little ambiguous anyway.

Using specific words is cultural. There are languages were in order to say a big number you just enumerate its digits.

Such as Tongan: http://www.sf.airnet.ne.jp/ts/language/number/tongan.html

Do you know of another unrelated language that works similarly?

A number of people (well, maybe at least 0xF people) have made suggestions about this: https://duckduckgo.com/?q=pronounce+hex+digits

> binary, the most fundamental number system

I think base 1 is a little more fundamental than base 2, no?

Mathematically speaking, base 1 doesn't make any sense. Using 1 as a radix yields something incoherent. But I think you mean simply making a mark for every unit (like how most people count inventory) which is definitely more fundamental in a different way.

I mean

    1 dec == 1 unit (1x1^0)
    2 dec == 11 unit (1x1^0 + 1x1^1)
    3 dec == 111 unit (1x1^0 + 1x1^1 + 1x1^2)

etc. Just like the other bases, with "1" instead of "2" or "10".

Well, maybe not "just like", the digit I have to use to represent each power of 1 is 1 and not 0, but I think that's a small concession.

That's not a "base". In base-n, the valid digits are 0..[n-1].

In your system, 1 = 10 = 100 = 1000, and 11 == 101 = 110, and 101 = 1+1 = 11. It's useless as a notation for arithmetic resembling like what bases are used for.

In base 1, the only valid digit is 0, so the only valid number is unit.

Right, I addressed that in my post...

writing ten like 1111111111 seems obvious enough, dividing by 11111 being 11 is alsof easy... but how fractions? Say 1 divided by 11111? I cant even imagine.

Unary is just tallies. Without the cross every fifth digit, of course.

The most efficient number system is ternary. If you go for balanced ternary you also get addition and subtraction for free, and multiplication is not much worse than for binary.