Example 1 Let $f(x)=\sum_{0}^{5}\left[2^{i} x\right]$. Find $f(3.14)$.
Given: $\because x=3.14, \frac{4}{2^{5}} \leqslant 0.14<\frac{5}{2^{5}}$, so take $p=3, k=4$.
$$
\begin{aligned}
\therefore f(3.14) & =\sum_{0}^{5} 2^{i} \times 3+\sum_{0}^{5}\left[\frac{4}{2^{i}}\right] \\
& =3 \times 63+7=196 .
\end{aligned}
$$