Prof. Murtagh,
My first Q is about Part 1, #4. If you were using 16-bit color instead of 8-bit, would you have to have a much bigger pallet that you need to have memory for (if an 8-bit pallet is made up of 2^8 colors, would a 16-bit pallet be 2^16?)?
My second question is about part 3. As far as I understand the problem, changing the value of r is only going to change the amplitude of the sine wave. Is there something else that I am supposed to be seeing or does changing the amplitude give the wave some advantage that I don't know about?
Thanks.

You have the right idea. The palettes used if 16-bit color were based on palettes could be much larger that those used with 8-bit color. To be precise, an 8-bit palette need not be exactly 2^8 colors long. It can be 2^8 or any smaller size. Similarly, if we used palettes with 16-bit color, they could be 2^16 colors long or shorter.

You also seem to understand the intent of the third question. The best hint I can think of to give you as to the "advantages" is to think back to Manchester encoding.

Tom