Example 2 Let
$$
\begin{aligned}
B= & \frac{a}{|a|}-\frac{b}{|b|}-\frac{c}{|c|}+\frac{d}{|d|}+\frac{a b}{|a b|}+\frac{a c}{|a c|}- \\
& \frac{a d}{|a d|}-\frac{b c}{|b c|}+\frac{b d}{|b d|}+\frac{c d}{|c d|}+\frac{a b c}{|a b c|}- \\
& \frac{a b d}{|a b d|}-\frac{a c d}{|a c d|}+\frac{b c d}{|b c d|}-\frac{a b c d}{|a b c d|} .
\end{aligned}
$$

Find the value of $B$.
$$
\begin{array}{l}
B=1-\left(1-\frac{a}{|a|}\right)\left(1+\frac{b}{|b|}\right)\left(1+\frac{c}{|c|}\right)\left(1-\frac{d}{|d|}\right) \\
=\left\{\begin{array}{ll}
1, & a, d(b, c) \text { at least one is positive (negative) ; } \\
-15, & a, d \text { are both negative, and } b, c \text { are both positive. }
\end{array}\right.
\end{array}
$$