The application of gray-scale digitizers to digitization of binary images of straight-edged planar shilhouettes is considered. A measure of digitization-induced ambiguity is introduced. It is shown that if the gray levels are not quantized and the spatial sampling resolution is sufficiently high, error-free reconstruction of the original binary image from the digitized image is possible. When the total bit-count for the representation of the digitized image is limited, i.e., sampling resolution and quantization accuracy are both finite, error-free reconstruction is usually impossible. In this case a bit allocation problem arises, and it is shown that the sensible bit allocation policy is to increase the quantization accuracy as much as possible once a "sufficient" spatial sampling resolution has been reached.