Proof of Uncomputability of Kolmogorov complexity

I was reading the page:

http://en.wikipedia.org/wiki/Kolmogorov_complexity

in particular the proof of why kolmogorov complexity is not computable.
Does anybody know why to encode n0 it takes log(n0) bits ? I'm
wondering because your programming language could represent numbers not
as regular numbers but as "1111" represents 4 and "111111" represents
6. Therefore you would need n0 space in the program to store n0 not
log(n0)... Basically the proof is assuming how n0 is stored.. is it
not ?

Thanks.

.

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