r and (r-1) complements
The basic point is that 2's complement simplifies things because you can use an adder to easily implement subtraction, this is because with 2's complement you have 

$$-B = \overline{B} + 1$$

so if you have to perform the operation \$A - B\$ you can easily evaluate it by evaluating \$A + \overline{B} + 1\$.