with 10 bit resolution has an input range of 0-5 V. How can I determine what digital output value will represent a certain voltage input?

 

10 bit resolution implies there are 1024 possible combinations ... 0 to 1023.

5 volts would be 1111111111. 0 volts of course would be 0000000000.

5 / (2^10-1) would give you the voltage per bit. For your example, it's 4.9 mV per bit.

So .... if you have 2.5 volts, that's 510 decimal or 0111111110 base 2

Now ... what is 1.254 Volts using your parameters?