Question

I am a Java beginner and pretty confused with this.

How is System.out.println(4*2147483647) equal to -4 in java?

Answer 1

It is due to integer silent overflow.

2147483647 == Integer.MAX_VALUE is the maximum value for an integer.

Silent overflow means that 2147483647 + 1 == Integer.MIN_VALUE = -2147483648
You can then see that 2147483647 + 2147483647 == 2147483647 + (-2147483648 + - 1) == -2

In other words, 2147483647 * 2 == -2, and you can now see why 2147483647 * 4 == -4.

More technically, the result is defined by the Java Language Specification #15.17.1:

If an integer multiplication overflows, then the result is the low-order bits of the mathematical product as represented in some sufficiently large two’s-complement format. As a result, if overflow occurs, then the sign of the result may not be the same as the sign of the mathematical product of the two operand values.