# Sample Resolution

Sample resolution (the number of bits per sample) determines how many gradations of amplitude (corresponding to loudness) can be represented in the digital waveform. The range of amplitudes from the most negative possible sample value to the most positive is referred to as the dynamic range and is normally expressed in decibels (dB) relative to the smallest non-zero digital value (i.e., 1). For example, with 16-bit resolution, the largest positive value representable is 32,767 and the smallest value representable is -32,768 giving a total range of 65,536 values or about 96 dB.
The conversion from linear amplitude values to decibels is defined as 20.0 times the logarithm of the linear value divided by the scale reference level. In this case, the reference level is 1 so: ``` 20.0 * log10(65638 / 1) = 96.3 ```
The next figure illustrates the effects of varying sample resolution. An analog sine wave is sampled at moderate resolution (circles correspond to about 6 bits resolution) and at very coarse resolution (asterisks correspond to about 3 bits resolution). While the higher resolution samples approximate the shape of the waveform fairly closely, the low resolution samples give a coarse, stair-step, approximation to the original waveform shape. 