how many steps the level is cut into, what a bit adds, and why floating point is not the next row
Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.
Three sizes in one archive — from a sheet on the fridge to a poster on the wall.
Signal to noise is for a full-scale sine wave with uniform quantisation. 16 bits are IEC 60908; 20 and 24 are named in table 1 of EBU R68-2000.
Bit depth does not make sound «better» — it sets how many steps the span between silence and full scale is cut into. Every added bit doubles that count, and a doubling of a ratio is 6.02 decibels. That is why the step between the rows of the table is the same everywhere, and no converter changes it: this is arithmetic rather than build quality.
The 1.76 in the formula is not pulled out of the air. A full-scale sine wave has an RMS value smaller than its amplitude by the square root of two, while uniform quantisation noise has one step divided by the square root of twelve. The ratio of those two gives 20 lg(2^(n−1)·√6), that is 6.02 n plus 1.76 at any depth.
Floating point does not go into that formula, and this is the most common mistake on the subject. In binary32 the significand is 24 bits — exactly as many as the widest fixed-point scale — so it resolves just as finely and no finer. The span of normal numbers really is about 1 529 dB, but that is a range of writable magnitudes, not a signal-to-noise ratio.
Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 7 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.
