A bit of background information: I plan to start experimenting with digital signal processing on microcontrollers. The particular microcontroller I plan to use (TI Stellaris LM4F230H5QR, from the Stellaris Launchpad) has a 12 bit ADC integrated on it, while on the other hand, all DACs I that look like possible candidates for me to use are 8 bit.
Obviously, before getting the output, I'll have to reduce the bit depth somehow. I could just get an 8 bit ADC and avoid the issue altogether, but I'd like to keep as much of the signal processing line at 12 bits as I can.
First, am I right in my assumption that by keeping 12 bits for as long as I can, I'll get better results?
Second, is there a smarter way of turning those 12 bits into 8 bits than just shifting everything to the right four times?