Bit depth refers to the number of digital bits used to represent the signal and is a measure of the data resolution.
For linear PCM represented using \"fixed-point\" data (this is explained below), each bit provides about 6dB of resolution. 16-bit data (used on CDs) has about 92dB of range, 20-bit has about 116dB, and 24-bit has about 140dB. 32-bit data is typically \"floating-point\" (also explained below), and has 25-bits of resolution (about 146dB).
The number of digital values available to represent a signal using n-bits is 2^n (\"two raised to the n-th power\"), or 2 multiplied by itself n-times. A 16-bit signal has 65536 different values.
If the actual signal values don't exactly match the available digital values, errors are introduced into the signal. These errors are called \"quantization noise\". The more bits you have, the lower the quantization noise. Dither can be used to reduce the perceived level of this noise and increase the effective resolution.
Audio has a wide dynamic range. The peak levels of the loudest section of a track can be many dB above the average level, and the quiet sections can be tens of dB below the average level.
A brick-wall limiter set on turbo-squash will still have peaks about 6 to 9dB above the average level (the hottest of hot masters will have peaks only 3 to 4dB above), while uncompressed material typically has peaks 12 to 18dB above the average level. This difference between the average and peak levels is the \"headroom\".
Digital audio can be represented as either fixed-point or floating-point data. Fixed-point data means each bit has a fixed value, while floating-point data can scale the range of values up or down as needed to maintain resolution when the signal level changes.
Fixed-point data is used for all data sent or received from A/D and D/A converters, and by some DSP systems (like those based on the Motorola 56K chip); fixed-point data can have many different resolutions from 16- to 24-bits used by converters, and 24- to 48-bits used by DSPs.
Floating-point data is used by most native DAWs, and by some DSP systems (like the UAD-1 and Creamware Pulsar); Floating-point data can have resolutions from 32-bits (equivalent to 25-bits of fixed-point resolution) up to 160-bits.
Fixed-point systems must reserve the upper bits of the digital signal for headroom to avoid clipping, so their effective resolution is reduced. Likewise, in quiet passages, fixed-point systems lose even more resolution as the level drops further below the peak level. That's why it's very important to maintain proper signal levels when recording or using fixed-point DSP systems.
Floating-point systems don't have these limitations, and use all the available bits to represent the signal, thus providing much better resolution than fixed-point systems. They're also free from internal clipping, and the noise floor drops with the signal level.
Regardless of whether you process your audio in fixed- or floating-point, you will eventually need to output fixed-point data, often at a lower resolution than your processing system. This is why proper mastering is important.
-Joe
