This may be a case of you can't have your cake and eat it too.
Based on the conclusions by CodingBadly, there are in fact 1024 steps and each step covers a voltage range. So what voltage value do you choose to ouptut?
Step (count) 0 0 to 4.8828124mV
Step (count) 1 4.8828125 to 9.765624
...
Step (count) 1023 4.9951171875 to 5.0 V
If you make step 0 output 0mV, and step 1 output 4.8828125mV, then step 1023 would output 4.9951171875V. The ADC would never return an output of 5V.
How do you justify step 0 output the "lower bound" of the range and the last step output the "upper bound" of the range?