What “signed” means in the context of sound / adio file formats?

Question

I'm learning how to use sox and i encountered this explanation:

We can also use sox to convert a raw file to another format. In this case, we have to supply some information about the raw file:

sox -r 44100 -s -w foo.raw foo.wav

The three flags preceding the input file name tell sox that the input file has a sampling rate of 44,100 samples per second, that the data is signed, and that each sample consists of a two byte word ...

What signed means in this context? The paragraph above is from here.

Answer 1

Signed and Unsigned refer to how numbers are stored for the samples. A sample corresponds to voltage above or below 0.

Signed data is a format that can store negative numbers, so 0 is no voltage and positive or negative numbers can be used to describe the direction of the voltage.

In unsigned data, all numbers are positive and the middle of the range is used for 0 volts.

This refers to the same kind of signed/unsigned used in computer programing when dealing with integer values.

Answer 2

Signed data in audio just means that a value of 0 corresponds to a voltage of 0V and the number being interpreted in two's complement.

Unsigned data means that the lowest (negative) and highest (positive) voltage are represented by all zeros and all ones, with 0V being in the middle of the range (what would be the most negative number in two's complement). You can switch from one representation to the other by flipping the most significant bit in a word.