Converting 8 bit sound into 2 bit sound

Question

How can I convert an 8-bit raw sound file into 2 bit sound? I want to test a 2-bit DAC I made with some real speech recording.

Here is what I have currently:

0x7e, 0x7e, 0x7b, 0x7b, 0x7b, 0x7b, 0x7a, 0x7a, 0x77, 0x77, 0x76, 0x76,
0x78, 0x78, 0x79, 0x79, 0x79, 0x79, 0x7b, 0x7b, 0x7d, 0x7d, 0x7e, 0x7e,
0x80, 0x80, 0x82, 0x82, 0x82, 0x82, 0x81, 0x81, 0x81, 0x81, 0x81, 0x81,
0x80, 0x80, 0x7e, 0x7e, 0x7d, 0x7d, 0x7c, 0x7c, 0x7a, 0x7a, 0x7a, 0x7a, ...

This is the 8-bit data of raw format converted into a hexadecimal string. Is taking the 2 MSBs of this data okay(for 7 it is 01(binary) and for 8 it is 10(binary) Is that okay?)? or do I have to somehow normalize this? Is there any program(I couldn't find 2-bit exports anywhere I looked) that can convert a sound (in whatever format) to 2-bit raw binary?

Edit: I found a related question which approaches this problem from a different angle.

How to record wav file in bit depths lower than 8 bit?

Answer 1

Taking the 2 MSBs should be just what you're after. The way I think of it is that 1 bit (1 or 0) simply tells it the signal is above or below the middle value - and since we're talking audio, that would be the zero line.

So, 2 bits would do the same, but subdivide the range into 4 'zones'. 3 bits into 4 'zones' and generally, x bits = 2^x 'zones'.