Java – multiplication overflow of two ints results in negative numbers

Consider this fragment in the Java language specification

class Test {
    public static void main(String[] args) {
        int i = 1000000;
        System.out.println(i * i);
        long l = i;
        System.out.println(l * l);
    }
}

Output is

-727379968
1000000000000

Why the result of (I * I) is - 727379968? Ideally, it should be 10000000000

I know that integer ranges from - 2147483648 to 2147483647 So obviously, 10000000000 is not in the given range

Why did the result become - 727379968?

Solution

Java (most computer architectures today) uses something called two's complexity arithmetic, which uses the highest bit of an integer to indicate that a number is negative If you multiply by two big numbers, you end up with such a big number, it sets the highest bit, and the result is negative