In one's complement flipping the bits of a number is equivalent to multiplying by -1 in base 10. Not really, since it is a positive number in all of the representations. On the other hand, it gets most additions correct. In two's complement flipping the bits and adding 1 is equivalent to multiplying by -1 in base 10. It appears as if things are good with two's complement.
All additions work correctly.
This is the representation used by modern computers. We assumed a computer can't dynamically add more bits to its numbers. Thus, it is important to know the size of numbers that can be represented with some number of bits. The number of negative numbers is one more than the number of positive numbers. From the examples, this is obviously not the case when adding two's complement numbers.