1 A. When $2^{k} \leqslant m<2^{k+1}(k \in \mathbf{N})$, $f(m)=k$, so
$$
\begin{aligned}
& f(1)+f(2)+\cdots+f(1024) \\
= & 0+1 \times 2+2 \times 2^{2}+\cdots+9 \times 2^{9}+10 \\
= & 2\left(1 \times 2+2 \times 2^{2}+\cdots+9 \times 2^{9}+10\right)-\left(1 \times 2+2 \times 2^{2}+\cdots+9 \times 2^{9}+10\right) \\
= & 9 \times 2^{10}-2^{9}-2^{8}-\cdots-2^{2}-2+10 \\
= & 8 \times 2^{10}+12 \\
= & 8204 .
\end{aligned}
$$
1 Let $m \in \mathbf{N}, \log _{2} m$'s integer part is denoted by $f(m)$. Then the value of $f(1)+f(2)+\cdots+f(1024)$ is
A. 8204
B. 8192
C. 9218
D. 8341