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

Lets look at the binary:

1000000 is 1111 0100 0010 0100 0000.
1000000000000 is 1110 1000 1101 0100 1010 0101 0001 0000 0000 0000

However, the first two sections of 4 bits won't fit in an int (since int is 32-bits wide in Java,) and so they are dropped, leaving only 1101 0100 1010 0101 0001 0000 0000 0000, which is -727379968.

In other words, the result overflows for int, and you get what's left.