Ay ay ay. Here's yet another worry to give you headaches.
One of the examples explored the properties of an algorithm, described in an IBM Knowledge Center document designed to convert a binary field representing the number of counts of a quartz oscillator to integers for digital display.2 In Ref. 1, it was demonstrated that the algorithm was vulnerable to rounding error resulting in an incorrect digital display. Investigation associated with this example forms the focus of this note.
The timing simulation results presented in Ref. 1 suggested that uncorrected rounding error in stopwatch timer displays could be impactful if used for precision timing, such as for race times or in experimental physics. Here, we present and analyse race times obtained from swimming competitions. The data give a clear demonstration of anomalous stopwatch timing patterns, which can only be explained by rounding error. It is also shown that such rounding error can result in a set of times being wrongly ordered. In the context of a sporting event, this could lead to the incorrect ranking of athletes and hence the incorrect awarding of race positions. As a spin-off of Ref. 1, this note may be of interest to educators, with the results providing a resource for discussion and the approach providing a template for additional student projects.