hi George,
If you are really determined on getting full 10-bit resolution across the range of 4.0v to 4.5v it is possible. However, it would require adding some external hardware. The way it’s done is by subtracting 4.0v from the bottom of your scale & then scaling the remaining 0.5v (i.e. 4.5 - 4.0) to be 0 …+2.047v (= internal Picaxe Vref) into a Picaxe analog input. I have done something similar because I wanted to use the AC712-30 sensors for amp readouts but was not interested in measuring negative current (meaning I had to subtract ~2.5v from the bottom of scale).
I scaled for 0…30 Amps = 0…+3.0 Vout so I could read amps directly on a DVM. I believe I changed Rz to 1.5Meg for this scaling. The 0..+3.0v was then scaled to Picaxe 0…+2.047v into the Picaxe AIN. Why did I use the ACS712s rather than shunts? Well they were dirt cheap on Amazon (sorry, no fancy technical reason).
If it’s really important enough for you to go to that much trouble, see the attached .pdf. If anyone is interested enough, I could post the project. There are some situations where it’s useful to “saw off” the bottom portion of an incoming voltage & scale the remaining voltage to fit the 10-bit resolution offered by the Picaxe. The Picaxe AIN IS very accurate.
Note that since you want to subtract 4.0v (rather than 2.5v) the values in the attached .pdf might have to be re-scaled.
Depending on your background, this might be somewhat interesting or give you a headache.
Good luck with your project!