AIME 1994 Problem 4

Find the positive integer $n\,$ for which $$\lfloor\log_2{1}\rfloor+\lfloor\log_2{2}\rfloor+\lfloor\log_2{3}\rfloor+\cdots+\lfloor\log_2{n}\rfloor=1994$$ (For real $x\,$, $\lfloor x\rfloor\,$ is the greatest integer $\le x.\,$)