  We present a binary code for spinors and Clifford multiplication using
non-negative integers and their binary expressions, which can be easily
implemented in computer programs for explicit calculations. As applications, we
present explicit descriptions of the triality automorphism of $Spin(8)$,
explicit representations of the Lie algebras $\mathfrak{spin}(8)$,
$\mathfrak{spin}(7)$ and $\mathfrak{g}_2$, etc.
