We discuss the optical conductivity of several noninteracting two-dimensional semiconducting systems focusing on gapped Dirac and Schrodinger fermions as well as on a system mixing these two types. Close to the band gap, we can define a universal optical conductivity quantum of sigma(0) = 1/16 e(2)/(h) over bar for the pure systems. The effective optical conductivity then depends on the degeneracy factors g(s) (spin) and g(v) (valley) and on the curvature around the band gap nu, i.e., it generally reads sigma = g(s)g(v)nu sigma(0). For a system composed of both types of carriers, the optical conductivity becomes nonuniversal.