Just for the record, it happens that unsigned integers and 2's complement integers can use the same addition rules (in binary) but they have to use different tests to determine whether anything anomalous occurred.
For instance, if you have 8-bit pattern 1111 1111 and you add 0000 0001 to it, you get bit pattern 0000 0000. But the first question is whether this was a signed or an unsigned number. What you do is look at individual column overflows, or carries. Binary addition of two operands involves 4 bits per column. Two bits for the binary digits that are in the operands, one bit for the binary digit that is your answer, and one bit for overflow. (Because 001 + 001 is actually 010, because the left-most column produced a 0 and an overflow that carried into the next column.
To finish this long story, if you have signed numbers, then the most significant bit (MSB) is the sign bit. You had an overflow if the carry into and out of the MSB DON'T match.
If you had unsigned numbers, then you had an overflow when the carry out of the MSB (which is NOT the sign bit... unsigned, remember?) was 1.
The part that is significant is that if you use 2's complement, there is no special logic required for the binary adder. 2 addends, a sum, and a carry bit for each column. Same rules for each. And rather than worry about subtraction logic, the CPU just internally generates the 2's complement of the number and then adds it. So a SUBTRACT hardware instruction is internally (usually) implemented as NEGATE, ADD (in that order.)
The REAL fun is that with a binary shifter and the 2's complement adder, you can also do multiplication. But I'll leave that exercise for the curious insomniacs among you.
