I'm working through the example on this page: http://chimera.labs.oreilly.com/books/1234000001552/ch03.html
I totally understand why the maximum level of an audio system would be 0 because the log of 1 is 0.
However, I'm confused about the minimum. The definition of dBFS is
dBFS = 20 * log( [sample level] / [max level] )
In a 16 bit system there are 2^16 = 65536 values. So this means values from -32768 to +32767. Excluding 0, let's say the minimum value is 1. So plugging this into the formula gives:
dBFS = 20 * log( 1 / 32767 ) = -90.3
But the book is saying it should be -96dBFS. Where am I going wrong?