The most typical type of spinor, the Dirac spinor, is a member of the fundamental representation of the complexified [Clifford algebra]? C(p,q), into which Spin(p,q) may be embedded. In even dimensions, this representation is reducible when taken as a representation of Spin(p,q) and may be decomposed into two the left-handed and right-handed Weyl spinor representations, which may be distinguished only by the action of parity transformations (not part of Spin(p,q), but present in C(p,q)). In addition, sometimes the non-complexified version of C(p,q) has a smaller real representation, the Majorana spinor representation. If this happens in an even dimension, the Majorana spinor representation will sometimes decompose into two Majorana-Weyl spinor representations. Of all these, only the Dirac representation exists in all dimensions.
A 2n- or 2n+1-dimensional Dirac spinor may be represented as a vector of 2n complex numbers.
Ok, now just tell us how to represent such thing on a computer and we'll be happy. --Taw