• zero - nothing happened
• one - an event occurred

A string of ones and zeros taken from a simulation of radioactive decay

Converting this into a sound file turns out to be really simple. A normal loudspeaker will respond to a very steep and very high change in its input signal with the kind of click we want to create. So all we had to do to create the sound of the Geiger counter was converting the string of ones and zeros into a string of minimum and maximum input value (usually 1..255) of a sound converter and feeding that into the converter.
Adding clicks to existing soundfiles is just as simple. In the sonification of the damped harmonic oscillator we added a click every time the oscillator would pass the x-axis. Whenever the oscillator passed the x-axis we added the sequence 1,255 which will always create a click regardless of what the values right before and right after it are.

A click added to an otherwise smooth, sinusoidal soundfile.