A binary encoding of spinors and applications

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 $\mathfrak{s}\mathfrak{p}\mathfrak{i}\mathfrak{n}(8)$, $\mathfrak{s}\mathfrak{p}\mathfrak{i}\mathfrak{n}(7)$ and ${\mathfrak{g}}_2$, etc.