If you have a ruler and it goes to 12 inches, you should normalize by the length L and not by 13, the number of points on the ruler.
the correct way is to use a slide rule
But who says that the numbers are representing the points, rather than representing the intervals between the points?
I'm confused by that analogy. Is the “ruler” a 255-inch ruler with 256 points labeled 0–255, or is it a 256-inch ruler with 256 1-inch segments, making L = 256×1?