AHSME 1975 Problem 18

A positive integer $N$ with three digits in its base ten representation is chosen at random, with each three digit number having an equal chance of being chosen. The probability that $\log_2 N$ is an integer is $\textbf{(A)}\ 0 \textbf{(B)}\ 3/899 \textbf{(C)}\ 1/225 \textbf{(D)}\ 1/300 \textbf{(E)}\ 1/450$