1996 AIME Problem 2

For each real number x, let \lfloor x \rfloor denote the greatest integer that does not exceed x. For how many positive integers n is it true that n<1000 and that \lfloor \log_{2} n \rfloor is a positive even integer?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.