Convert $(2175)_{8}$ to a binary number.
Using the formula in (2.2), we have
$$\begin{array}{ll}
(2)_{8}=(010)_{2}, & (1)_{8}=(001)_{2}, \\
(7)_{8}=(111)_{2}, & (5)_{8}=(101)_{2},
\end{array}$$

thus we get
$$(2175)_{8}=(010001111101)_{2}=(10001111101)_{2}$$