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In this paper, we proposed a new image quality evaluation index-color distribution index (CDI). It considers color gamut, contrast ratio, maximum luminance, gamma characteristics, and just noticeable difference (JND) as human visual system to evaluate the ability for reproducing visually smooth gradation. When the CDI cell was defined, we verified JND from a fundamental matter, such as JND in luminance and chromaticity, using the latest TV sets. According to our investigations, luminance JND was AL/L = 0.01 and chromaticity JND was Au'v' = 0.001. We used these with unit CDI cell and evaluated bit depth needed for high image quality without any visible false contour. We clarified that 12 bit is needed for necessary and sufficient condition to reproduce high image quality with TV set designed based on BT.709. Also, we clarified that color gamut, contrast ratio, maximum luminance, gamma characteristics and bit depth should be balanced to achieve TV sets of high image quality from the viewpoint of the total image quality improvement.