How does delta modulation work practically?
One key point to note about delta modulation schemes is that they quantize the change between the current value and the previously quantized value.



The other key point to note is that, in general, delta modulation schemes are run at sampling rates MUCH higher than the Nyquist rate would suggest. Early portable CD players used a scheme called MASH (multi-stage noise shaping) on their DACs to allow cheaper, more accurate reproduction of sound.

I can't find a reference quickly, but I seem to recall that for the 44.1kHz CD sampling rate, MASH 1-bit DACs ran at sampling rates in the order of 5-6 MHz.