In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz's original publication [PRL 80 209 (1998)] this universality has been verified for a variety of continuous time systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process, thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function properly characterises the large system size limit of a single particle discrete time system, even in the case of very small system sizes. This property serves to further increase the ease and accessibility of our method allowing us to directly study even more challenging dynamics and verify the Derrida-Lebowitz scaling function for the multiple particle discrete time asymmetric exclusion process as well.