Suppose, I have a simple method:
public int add(int a, int b) {
return a + b;
}
If I run it with max int values
add(2147483647, 2147483647);
I get -2. I found that if we overflow int then we go to min integer value (-2147483648) and keep adding.
Let's do some math. If I add 2147483647 + 2147483647 I should get -1, because
-2147483648 + 2147483647 = -1
So why do I get -2?
Think of it like this:
2147483647 + 2147483647
= 2147483647 + ( 1 + 2147483646 )
= ( 2147483647 + 1 ) + 2147483646
= -2147483648 + 2147483646 // Because of overflow
= -2
That is, to get the lefthand 2147483647 to overflow, you had to add 1 to it. That 1 came from the right-hand 2147483647, so now there is only 2147483646 left.
Of course, internally it's done by 2s-complement addition, not by adding 1s until you reach the end. The above just clarifies the maths.
Lets do some math. Max is 2147483647 but min is -2147483648.
2147483647 + 1 = -2147483648
2147483647 + 2 = -2147483647
...
2147483647 + n = -2147483648 + n - 1
which for n = 2147483647 gives us
2147483647 + 2147483647 = -2147483648 + 2147483647 - 1 = -1 - 1 = -2
