Digital audio editing programs can often use sample sizes above their final product's bit depth. Standard samples sizes of 20-bits, 24-bits, even 32-bit floating-point or long integer samples are now common, used to minimize fractional values and their attendant noise introduced when mixing or engaging in other mathematical processes on the samples. Another reason higher bit-depth recording is becoming more attractive, as prices come down and storage becomes less of an issue, is that quantization errors are much more critical at lower amplitudes, due to the linear amplitude divisions of the PCM quantization process. At very low amplitudes, these errors are much more apparent, acting more like distortion than noise. Therefore, it is still highly recommended that you record at sufficient overall amplitude to reduce quantization error as much as possible. Normalizing your overly soft tracks after they have been quantized only compounds the issue.
Higher bit-depth files can be reduced back to 16-bit for things like CD burning. This process is often enhanced by using a process called dither, which tries to minimize the inducement of further digital noise and harmonic distortion caused by simple truncation. Dither allows higher bit depths, such as 20- and 24-bit files to be reduced to 16-bits by not doing the obvious, which would be rounding off the extra precision to the nearest 16-bit value. Instead, it combines the least significant bits below the most significant 16 with random values, then rounds up or down to the nearest 16-bit value. Click here for a fuller explanation of dither.
As mentioned above, if you don't record above 16-bit resolution, try to adjust recording levels to avoid prolonged periods of very low amplitudes while not exceeding the maximum amplitude of the system at peaks. Digital systems do not provide the fuzzy headroom of analog systems—they just run out of values and clip. Most DAWs now come with multiple forms of distortion plug-ins to recreate the sound of overdriven analog tube electronics and over-saturated tape recordings without resorting to the less musically attractive and unsatisfying results of digital clipping.
dBFS (decibels relative to full scale (digital)) is a measurement of digital amplitude relative to the maximum sample value, and is therefore relative to sample size. 0 dBFS is set to the maximum value, and values below that are negative. For a 4-bit sample with 16 values, a steady-state signal with a maximum amplitudes between unsigned 0000 and 1111 would be considered to be at 0 dBFS, while half that digital amplitude (8 values), between unsigned 0000 and 0111 would be -6 dBFS. dBFS can also be used to express the noise floor of a signal relative to a full-scale sine wave. A 16-bit system (without dither) has a theoretical minimum noise floor of approximately -98 dBFS.