How to return middle bits from random number generator?

I have a random_rand() function which produces a random number between 0 and RANDOM_RAND_MAX. RANDOM_RAND_MAX is defined to be 65535.

I would like to use the middle bits from the result of random_rand() instead of lowest-order bits so that I can make the randomiztion better.

Could you please show me a quick way to do this.

Thanks