replaces it with a constant, fixed noise level. The final version of audio that goes onto a compact disc contains only 16 bits per sample, but throughout the production process, a greater number of bits are typically used to represent the sample, this must be reduced to 16 bits to make the CD. There are multiple ways to do this. One can, for example, simply discard the excess bits – called truncation. One can also round the excess bits to the nearest value. Each of these methods, however, results in predictable and determinable errors in the result. Using dither replaces these errors with a constant, fixed noise level. Examples Take, for example, a waveform that consists of the following values: 1 2 3 4 5 6 7 8 If the waveform is reduced by 20%, then the following are the new values: 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 If these values are truncated it results in the following data: 0 1 2 3 4 4 5 6 If these values are rounded instead it results in the following data: 1 2 2 3 4 5 6 6 For any original waveform, the process of reducing the waveform amplitude by 20% results in regular errors. Take for example a sine wave that, for some portion, matches the values above. Every time the sine wave's value hit 3.2, the truncated result would be off by 0.2, as in the sample data above. Every time the sine wave's value hit 4.0, there would be no error since the truncated result would be off by 0.0, also shown above. The magnitude of this error changes regularly and repeatedly throughout the sine wave's cycle. It is precisely this error that manifests itself as distortion. What the ear hears as distortion is the additional content at discrete frequencies created by the regular and repeated quantization error. A plausible solution would be to take the 2 digit number (say, 4.8) and round it one direction or the other. For example, it could be rounded to 5 one time and then 4 the next time. This would make the long-term average 4.5 instead of 4, so that over the long-term the value is closer to its actual value. This, on the other hand, still results in determinable (though more complicated) error. Every other time the value 4.8 comes up the result is an error of 0.2,