Example 1-3 The number of 0,1 symbol strings of length $n$ is $2^{n}$.

.
For $2^{n}=\underbrace{2 \cdot 2 \cdot \cdots \cdot 2}_{n \uparrow}$, for example $n=3$, we have
$$
000,001,010,011,100,101,110,111 \text {. }
$$

or represented as Figure 1-1.
Assuming $a=a_{1} a_{2} \cdots a_{n}, a_{i} \in[0,1], i=1,2, \cdots, n$, according to the multiplication rule, the number of 0,1 symbol strings can be immediately obtained.