The term "class-D" is sometimes misunderstood as meaning a "digital" amplifier. The quantization of the output signal at the power stage can be controlled by either an analog signal or a digital signal. Only in the latter case would an amplifier be using fully digital amplification.
http://en.wikipedia.org/wiki/Switching_amplifier
http://www.audioholics.com/education/amplifier-technology/the-truth-about-digital-class-d-amplifiers