I heard C, C++, Java uses two complements for binary representation. Why not use 1 complement? Is there any advantage to use 2 complement over 1 complement?
Working with two's complement signed integers is a lot cleaner. You can basically add signed values as if they were unsigned and have things work as you might expect, rather than having to explicitly deal with an additional carry addition. It is also easier to check if a value is 0, because two's complement only contains one 0 value, whereas one's complement allows one to define both a positive and a negative zero.
As for the additional carry addition, think about adding a positive number to a smallish negative number. Because of the one's complement representation, the smallish negative number will actually be fairly large when viewed as an unsigned quantity. Adding the two together might lead to an overflow with a carry bit. Unlike unsigned addition, this doesn't necessarily mean that the value is too large to represent in the one's complement number, just that the representation temporarily exceeded the number of bits available. To compensate for this, you add the carry bit back in after adding the two one's complement numbers together.