Suppose you took a digital picture of a poster that used onl…

Suppose you took a digital picture of a poster that used only sixteen distinct colors, and you want to compress it.  If your digital camera stores pictures using a color depth of 64 thousand colors (that is, 16 bits per pixel) you could save a lot of file space by reducing the number of bits used for each pixel. What would be the optimal number of bits to use?  Show your calculations.