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## Precision and Dynamic Range

The precision of digitally recorded values depends largely on the resolution of the conversion device, known as an Analog to Digital (A/D) Convertor. Typical A/D convertors produce samples of 8, 16, or 24-bit resolution.

Bit Dynamic Range
Resolution, bits Max Positive Value Max Negative Value
8 +127 -128
16 +32,767 -32,768
24 +8,388,607 -8,388,608

The sample values are integers with maximum and minimum values that depend on the number of bits per sample, as related in "Bit Dynamic Range"

One of the characteristics of audio that is most affected by the number of bits per sample is dynamic range. It is a term that describes the range of loud to soft audio levels that can be accommodated. The loudest (“full volume”) audio levels are represented by the maximum value that can be represented for a given number of bits per sample. These maximum values equate to the voltage levels of analog amplifiers at which the +/- output voltages reach the limits of the power supplies being used. If a +/- 30 volt power supply is being used, and ignoring output device losses, the output voltage can never exceed +/- 30 volts. If the input signal is increased beyond this, the waveform that would have been above the maximum limit is said to have been “clipped”. A clipped sine wave begins to look like a square wave at extremely over driven levels.

These maximum values are also the values associated with the term “0 dBFS”, which means “0 dB Full Scale”. It is an arbitrary “reference point” that simply means the maximum possible volume that can be represented for a given number of bits per sample (resolution). Therefore, the number of bits per sample determines the maximum values that can be represented, and the maximum values represent the maximum volume.

The lowest level that can be represented is the minimum possible non-zero number that can be represented, and that of course in all cases is the value 1, or -1.

The difference between the maximum and minimum representable values, expressed in decibels is defined as the “dynamic range”.

For any given sample value, Level in dBFS = 20 * LOG (level / max level). For example, for 8-bit samples the minimum level in decibels is: .

Bit Dynamic Range in dBFS
Resolution, bits Max Malue Dynamic Range
8 127 42 dB
16 32,767 90 dB
24 8,388,607 138 dB

Therefore, for 8-bit samples, the dynamic range is 42 dB, and "Bit Dynamic Range in dBFS" indicates the dynamic range for all number of bits per sample (resolution) discussed.

To help give these numbers some meaning, the human ear has a dynamic range of about 120 dB, and since Compact Disks (CDs) use 16-bit samples, they inherently have a dynamic range of 90 dB. The legacy telephone network uses 8-bit samples, and thus has a dynamic range of 42 dB