A computer does not directly produce loudness. (The amplifier does that.) What the computer produces is differences in amplitude, or the maximum displacement within a waveform.
As stated above, a 16-bit D/A converter accepts numbers between +32767 and -32768, and converts them into a continuously varying voltage. Thus, the maximum displacement (the difference between +32767 and -32768) is:
32767 - -32768 = 65536
Converting that number into decibels (a common way to measure magnitude):
20 * log10(65536) = 96.32 dB
So, the greatest magnitude that can be produced by a 16-bit converter is about 96 dB. By way of metaphor, the sound of people quietly talking in a room is about 60 dB, and the sound of an airplane taking off is about 120 dB.
(By the way, for the purposes of this discussion, it is not necessary that the reader understand the mathematical implications of logarithms. Rather, the salient point is to understand that this is a way of measuring the loudness of a waveform created by a computer.)
In the square wave example above, three numbers were being sent to the D/A converter: 30000, -20000, 16000, and -5000. The maximum displacement here is between +30000 and -20000, which is 50000. Converting this number into decibels:
20 * log10(50000) = 93.97 dB
or almost 94 dB, close to the maximum of what a 16-bit converter can produce.
If we wanted to produce a waveform whose maximum amplitude was 60 dB, then we would use the following formula:
10(60/20) = 1000
This means that the maximum displacement we need is 1000. So, a 60 dB waveform might look like this:
The number +500 is output for 20 samples, then -500 for 30 samples, +250 for 10 samples, and -250 for 40 samples. The maximum displacement is between +500 and -500, which is 1000.
The fundamental frequency of this waveform is the same as the waveform above (441 hertz). Only the loudness is now 60 dB rather than the 94 dB in the earlier example.