Digital zoom is cropping followed by re-sampling. Let's say you have an image that's 3200x2400 pixels, and the coin (or part of the coin you want to zoom) takes up the center 800x600 pixels. When you do a 4x digital zoom-in on those 800x600 pixels, the camera crops the image at 800x600, then up-samples the image to 3200x2400. All the potential image problems (due to noise, shake, lens aberrations, etc) are magnified 4x and the image quality suffers. The zoom algorithm has to interpolate between the actual pixels and the fictitious ones it must create to fill in the image to full size. The end result is that if you do a 4x zoom, only 6.7% (1/16, since both X and Y are zoomed by 4) of the image is "real", and the rest is a figment of the imagination of the zoom algorithm.