Digital cinema will continue, for some time, to use image signals converted from the density values of film stock through some form of digitization. This paper investigates the required numbers of quantization bits for both intensity and density. Equations for the color differences created by quantization distortion are derived on the premise that the uniform color space L* a* b* can be used to evaluate color differences in digitized pictorial color images. The location of the quantized sample that yields the maximum color difference in the color gamut is theoretically analyzed with the proviso that the color difference must be below the perceivable limit of human visual systems. The result shows that the maximum color difference is located on a ridge line or a surface of the color gamut. This can reduce the computational burden for determining the required precision for color quantization. Design examples of quantization resolution are also shown by applying the proposed evaluation method to three actual color spaces: NTSC, HDTV, and ROMM.