83 Let the set $S=\{1,2,3, \cdots, 100\}, S_{1}$ be any non-empty subset of $S$, and the difference between the largest and smallest elements in $S_{1}$ is called the "diameter" of $S_{1}$. Then, the total sum of the diameters of all subsets of $S$ with a diameter of 91 is
A. $91 \cdot 2^{91}$
B. $10 \cdot 91 \cdot 2^{91}$
C. $9 \cdot 91 \cdot 2^{92}$
D. $9 \cdot 91 \cdot 2^{90}$
83 D. Let $S_{1} \subseteq S, S_{1}$'s maximum element be $i$, and the minimum element be $j, 1 \leqslant j \leqslant i \leqslant 100$, then the diameter of $S_{1}$ is $i-j$. The number of such $S_{1}$ is $2^{i-j-1}$, thus the total sum of the diameters of all subsets with diameter 91 is
$$
\sum_{j=1}^{9} 91 \times 2^{90}=9 \times 91 \times 2^{90} .
$$