[Proof] Two's Complement representation is bijective

Hi there!

I need help with a proof that the Two's Complement's representation is unique -> There are no two representations of a number.

The following formula describes the Two's Complement: ,

where is the value of the binary number . n is the number of digits. For example:

.

So the (decimal) is (binary; one zero, not ten) in the Two's Complement representation.

I tried proving it with a proof by contradiction, but I didn't get very far.

Any help?

Thanks in advance,

BS