1994 AIME Problem 4

Find the positive integer n for which

\left\lfloor\log _{2} 1\right\rfloor+\left\lfloor\log _{2} 2\right\rfloor+\left\lfloor\log _{2} 3\right\rfloor+\cdots+\left\lfloor\log _{2} n\right\rfloor=1994

(For real x,\lfloor x\rfloor is the greatest integer \leq x.)