why Integer.MAX_VALUE + 1 == Integer.MIN_VALUE?

Question

System.out.println(Integer.MAX_VALUE + 1 == Integer.MIN_VALUE);

is true.

I understand that integer in Java is 32 bit and can\'t go above 2³

Answer 1

You must understand how integer values are represented in binary form, and how binary addition works. Java uses a representation called two's complement, in which the first bit of the number represents its sign. Whenever you add 1 to the largest java Integer, which has a bit sign of 0, then its bit sign becomes 1 and the number becomes negative.

This links explains with more details: http://www.cs.grinnell.edu/~rebelsky/Espresso/Readings/binary.html#integers-in-java

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The Java Language Specification treats this behavior here: http://docs.oracle.com/javase/specs/jls/se6/html/expressions.html#15.18.2

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

Which means that you can rely on this behavior.