Example 18 Find $(1111)_{2} \div(101)_{2}=$ ?
First, find the complement of the divisor $(101)_{2}$, which is $(011)_{2}=(11)_{2}$. Then add the complement $(11)_{2}$ to the dividend $(1111)_{2}$ to get
$$\begin{array}{r}
(1111)_{2} \\
+\quad(11)_{2} \\
\hline(10010)_{2}
\end{array}$$

Then subtract $(1000)_{2}$ to obtain the remainder after the first subtraction of the divisor, which is
$$\begin{array}{r}
(10010)_{2} \\
-\quad(1000)_{2} \\
\hline
\end{array}$$

Then add the complement $(11)_{2}$ to the remainder $(1010)_{2}$ and subtract $(1000)_{2}$ again to obtain the remainder after the second subtraction of the divisor, which is
$$\begin{array}{r}
(1010)_{2} \\
+\quad(11)_{2} \\
\hline(1101)_{2} \\
-(1000)_{2} \\
\hline(101)_{2}
\end{array}$$

Then add the complement $(11)_{2}$ to the remainder $(101)_{2}$ and subtract $(1000)_{2}$ again to obtain the remainder after the third subtraction of the divisor
$$\begin{array}{r}
(101)_{2} \\
+\quad(11)_{2} \\
\hline(1000)_{2} \\
-(1000)_{2} \\
\hline
\end{array}$$

It is clear that since it was subtracted three times in total and just completed, the quotient is 3. Finally, convert the decimal number 3 to binary to get $(11)_{2}$, so
$$(1111)_{2} \div(101)_{2}=(11)_{2}$$