Integer Overflow

Consider an 8-bit system. What happens when you add 1 to the maximum value of 255 (11111111 in binary)? An integer overflow occurs. The 8 bit result becomes 00000000 because only 8 bits are kept.

11111111
+00000001
---------
1 00000000   < 9th bit carry-out

The carry bit is then set in the CPUs eflags register, indicating that an overflow has occurred. Decisions can then be made by the CPU based on this flag.

The remainder can be calculated as follows on an 8 bit system:

(a + b) mod 256

On a 16-bit system:

(a + b) mod 2^16

and so on…