In this article we demonstrate that the so-called bursting production of molecular species during gene expression may be an artifact caused by low time resolution in experimental data collection and not an actual burst in production. We reach this conclusion through an analysis of a two-stage and binary model for gene expression, and demonstrate that in the limit when mRNA degradation is much faster than protein degradation they are equivalent. The negative binomial distribution is shown to be a limiting case of the binary model for fast ''on to off'' state transitions and high values of the ratio between protein synthesis and degradation rates. The gene products population increases by unity but multiple times in a time interval orders of magnitude smaller than protein half-life or the precision of the experimental apparatus employed in its detection. This rare-and-fast one-by-one protein synthesis has been interpreted as bursting.