Fixed Point and Floating Point

Fixed point has a hard ceiling, floating point has room to spare, and that shapes every mixing decision.

Related

HeadroomClippingBit Depth

The question

A sample can be an integer or a float. The first clips at full scale, the second shifts the decimal point, and the difference sets the headroom a mix needs.

How it works

Fixed point holds the decimal point in place, so a 24-bit integer has no room past full scale and summed tracks that cross 0 dBFS flatten. Float stores an exponent, so 32-bit float spans far beyond the ear and a path can pass 0 dBFS undistorted. Only the trip to a fixed-point device needs a return to range. Huge gains still accumulate error.

Settings and practice

Keep the mix bus at 32-bit float, leave 3 to 6 dB before the DAC or an integer export, and limit there. Do not let float headroom excuse hot tracks.

What to listen for

On the Beethoven Ninth score, hear many parts at once. In a quartet's loud chord, hear four voices stack. Push the bus past 0 dBFS and pull back: float hides it, a 16-bit export does not.

Common misconceptions

Float does not allow endless overs, because playback ends at a ceiling. It is not noise-free, only very quiet. Fixed point is not low fidelity, since 24 bit covers most recording. A 32-bit float file adds no detail the source lacked.

Sources

• 浮点与定点音频通路的差异，依 DAW 厂商公开文档核查，未抄文本
• Pohlmann, Principles of Digital Audio, DSP chapters — background checked, not quoted

Used for fact-checking only; all prose is original.