Question

Line 294 of java.util.Random source says

if ((n & -n) == n) // i.e., n is a power of 2
    // rest of the code

Why is this?

Answer 1

The description is not entirely accurate because (0 & -0) == 0 but 0 is not a power of two. A better way to say it is

((n & -n) == n) when n is a power of two, or the negative of a power of two, or zero.

If n is a power of two, then n in binary is a single 1 followed by zeros.
-n in two’s complement is the inverse + 1 so the bits lines up thus

 n      0000100...000
-n      1111100...000
 n & -n 0000100...000

To see why this work, consider two’s complement as inverse + 1, -n == ~n + 1

n          0000100...000
inverse n  1111011...111
                     + 1
two's comp 1111100...000

since you carry the one all the way through when adding one to get the two’s complement.

If n were anything other than a power of two† then the result would be missing a bit because the two’s complement would not have the highest bit set due to that carry.

† – or zero or a negative of a power of two … as explained at the top.