# Why Digitize Data?

• The Flip Side of Digitization: Common Misunderstandings.

There are a number of common misconceptions and errors connected with the use of digitized data. We list the most common here. As we have not yet discussed any digitization process, the goal is not (yet!) quantitative understanding of the problems, but rather an intuitive idea of what is going on.

• Number of significant figures.

Every digitization yields only a specific number of digits. Data processing programs do not necessarily recognize this. For example, suppose that we want to find the signal-to-noise ratio for an intensity measurement, and we digitize the signal to find that the number of photons observed during a measurement interval was 327183. What is the signal-to-noise ratio? We know it should be the square root of the number of photons observed. The calculator application that comes in Microsoft WindowsXP shows that 3271831/2 = 571.99912587345795698295097687708. Now, really, how can a 6 digit measurement result in an answer with 32 digits of precision? This is absurd. Arithmetically, of course, there's no problem, but since there's uncertainty in the original measurement, most of the digits are only arithmetic eye candy, not physical reality. One might say 3271831/2 = 572, and that would be defensible. However, that suggests that we know the signal-to-noise ratio to 3 significant figures, that it's 572, not 571 and not 573. That hardly seems credible for a single measurement. Saying S/N = 600 (only one significant figure) or 570 (2 significant figures) is probably better. This is a simple example, but ensuring that we only report significant figures, not arithmetic detritus, is critical.