Finding overflows during arithmetic operations

We know that data in computers have limited size. For example, integer may be limited to 4 bytes. So, while writing programs sometimes we might need to check for overflows to make sure that the resulting value fits the size. But finding overflows are easy.

Finding overflow during addition

Lets say you are adding number a and b. Lets say maximum value that the types of a and b can hold be MAX. Then we can check for overflow using following condition:

if ( (MAX - a) < b then the result overflows else not.

Finding overflow during multiplication

One example of its use is while computing factorial. Lets say you want to compute n!. But you also want to make sure that appropriate error is thrown when it overflows. This is also quite simple. Lets say again that the maximum value a data type can hold be MAX and you are multiplying a and b. The result overflows if MAX/a < b.