  We consider a construction of the fundamental spin representations of the
simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed
width integers. This gives the spin matrices as a Lie subalgebra of a
$\mathbb{Z}$-graded associative algebra (rather than the usual
$\mathbb{N}$-filtered Clifford algebra). Our description gives a quick way to
write down the spin matrices, and gives a way to encode some extra structure,
such as the real structure which is invariant under the compact real form, for
some $n$. Additionally we can encode the spin representations combinatorially
as (coloured) graphs.
