The distribution shown in this post is for base 10, but Benford’s Law includes distributions for other bases too. The wiki article linked in another comment goes into detail on that too.

If you were in Base 12 or something it would still lean towards 1 but the percentage would be a little different.

The percentages change. At the lower end, in binary every number that isn’t 0 itself starts with a 1.

This fact is actually used to save one bit in the format that computers usually use to store floating point (fractional instead of integer) numbers.