[gota]

Well, the number of digits tell you the sign of the number, right? It could save a sign bit

I think the ideal wikipedia page for this kind of thing has a 'Properties' section from which to start thinking about this

[misja111]

The bit saved for the sign is lost because you need more bits to represent a number.

[gota]

True, and it seems you actually need exactly one extra bit for all positive numbers