When reducing color depth and dithering with a 2 bit noise (with n=]0.5,1.5[ and output=floor(input*(2^bits-1) + n)), the ends of the value range (inputs 0.0 and 1.0) are noisy. It would be desirable to have them to be solid color.

Example: https://www.shadertoy.com/view/llsfz4

(above is screenshot of the shadertoy, picturing a gradient and both ends which should be solid white and black respectively, but are noisy instead)

The problem can be of course solved by just compressing the value range so that the ends get always rounded to single values. This feels bit of a hack though, and I'm wondering if there's a way to implement this "properly"?