java - Multiplication of two ints overflowing to result in a negative number

Question

Consider this snippet from 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);
    }
}

The output is

-727379968
1000000000000

Why is the result -727379968 for (i*i)? Ideally it should be 1000000000000.

I know the range of Integer is from –2147483648 to 2147483647. so obviously 1000000000000 is not in the given range.

Why does the result become -727379968?

Answer 1

Java (like most computer architectures these days) uses something called two's complement arithmetic, which uses the most significant bit of an integer to signify that a number is negative. If you multiply two big numbers, you end up with a number that's so big it sets that highest bit, and the result ends up negative.