Java results differ for (int)Math.pow(2,x) and 1<<x

Question

Why do the following two operations yield different results in Java for x = 31 or 32 but the same results for x=3?

int         


        

Answer 1

int is 32 bits in size and since it is signed (by default), the first bit is used for the sign. When you shift left 31 bits, you get the Two's Compliment, which is -(2^32). When you shift left 32 bits, it just loops all the way back around to 1. If you were to do this shifting with longs instead of ints, you would get the answers you expect (that is until you shift 63+ bits).