What is the 16 bit unsigned binary number for 65534?
What is the 16 bit signed binary number for -2?
Both are 16’b1111111111111110 = 16'hfffe
The difference lies in how these numbers are mapped to signal amplitude within the ADC. Therefore, it is important to consider the format in which the ADC transmits data and to perform the necessary conversions if your code operates with a different representation.
In a signed representation, the number 0 corresponds to the center of the ADC scale, which roughly aligns with the average signal level. In contrast, for an unsigned representation, the number 32768 corresponds to the center of the ADC scale.
As you can see unsigned number 0 is not equals to signed number 0 in context of ADC output format.
In reality, the situation is a bit more complex since there is no specific code that represents the center of the scale due to the even number of codes. However, for the sake of simplicity in processing, the AES17 standard considers the signed number 0 as the center of the ADC scale. While this results in an asymmetrical scale, it simplifies the signal processing, and the value -32768 in this standard is considered as exceeding full-scale, because 16-bit full scale of signed number range is assumed as -32767..+32767.
To make it more clear, here is table with numbers for 4-bit ADC.
1-st column is a signal value in signed decimal format (which is used for processing)
2-nd column is a hex ADC output with unsigned format
3-rd column is a hex ADC output with signed format
-8 0 8
-7 1 9
-6 2 a
-5 3 b
-4 4 c
-3 5 d
-2 6 e
-1 7 f
+0 8 0
+1 9 1
+2 a 2
+3 b 3
+4 c 4
+5 d 5
+6 e 6
+7 f 7
Sure, but if you had dithered instead of rounding you would have had a hard time finding any signs of those spurs at all, and yet you would have added around 1/2 a bit of noise to the signal.
I understand what you're saying, but I'm not sure this approach can yield the same effective results as rounding. Dithering might be preferable if random noise is more acceptable than stable spurs, but it depends on the specific requirements of the application.