The P53 system suppresses tumors by arresting cell cycle when chromosomal DNA is damaged to allow for specialized enzymes to repair the DNA breaks. When the damage is too severe to be repaired, then the P53 system induces apoptosis. The critical role of P53 in suppressing tumors is underscored by the observation that over 50% of all cancers involve a disruption of this system. In response to DNA damage, protein level of P53 and its antagonist MDM2 oscillate roughly out of phase with respect to each other. The response has been termed a “digital oscillator” because the average number of cycles increases with the amount of DNA damage, whereas neither the heights of the oscillation nor the period is strongly affected (Lahav et al., Nat Genet. 36(2):113-4, 2004). Such a response is in sharp contrast to damped oscillations or strictly analog behavior that was previously assumed for this system. However, generating dynamical systems with digital oscillations is not straightforward using typical small systems of nonlinear state equations. As previously suggested (Monk, Curr Biol. 13(16):1409-13, 2003), the robustness of oscillations can be increased with inclusion of a pure time delay to represent the processes involved in transcription, splicing, and translation. Intuitively, there is a delay of 20-30 minutes between the induction of a gene and the appearance of the active protein that is the gene product. Using standard dynamical systems analysis, the inclusion of the time delay has no effect on the location of the fixed points of the system, but there can be pronounced effects on the stability of fixed points and the shape and location of the nullclines in the phase space. Using P53 as an example system, we show that inclusion of the time delay produces a robust dynamical system with roughly digital behavior like the biological system.