6. (B).

For 2, 3, and 4-digit numbers, the number of positive integers sought is $9+2 \times 9^{2}+3 \times 9^{2}=414$.
In the numbers $1,2, \cdots, 2002$, the number of positive integers that have exactly one digit 0 in their binary representation is ( ),
(A) 495
(B) 414
(C) 324
(D) 243