This way the last segment has not the same length of the others, for sure is longer, and you don't know how is long because you can get the same value, 1023, also for 5.5V, maybe more, maybe less.In other words 1023 mean a value that is bigger than Vref-Vref/1024 (not Vref!) but you don't know how many is bigger.
The 5/1023 or 5/1024 thing give relatively close results. But should always be divide by Vrange/1024 for the voltage resolution. It's definitely not 5/1023.
Seems you have not read the above... see the graphs in post #123 you will see that dividing by 1023 is as legit as dividing by 1024 => it gives you one of the possible value
always gives you the entry point of the interval (0, 1.25, 2.50, 3.75) whereas dividing by 3 gives you a point somewhere within the interval (0, 1.66, 3.33, 5) which are not worse than the other values
There is no but...any voltage value in the interval corresponding to the digital value is as good as any other one... that's it.
Do that in the online calculator and see how many decimal places the result has.
The way it works is... 10 bit... 1024 levels. Level 1 to level 1024. Voltage range is 5V for the analog range. 1024 levels (steps) contains 1023 individual gaps..... just as 2 steps has 1 gap. We don't divide the 5V range into 1023 portions. Instead, we divide it by the total number of levels (ie. 1024).
That other set of values you mentioned..... ie. [(0, 1.66, 3.33, 5)] ..... the 1.66 is actually 1.666666666666666666 etc. and the 3.33 is actually 3.33333333333333333 .... which isn't very good, because they just keep going, right? Maybe for a mathematical exercise it is all ok. But from a hardware implementation perspective, that's not what they do (or want to do), right?