How do I convert a signal of 3v to 2v to a signal of 0 to 5 v
I would suggest just using a lower reference voltage rather than altering your signal. By using a lower reference voltage, your 1024 discrete points are spread over 0-3V rather than 0-5. In most cases, using the default reference voltage is fine, but sometimes the extra precision is needed. In order to do this, use a voltage divider with Vout=3V or slightly higher than the maximum voltage you ever expect to see, and connect the input to the VRef pin on the Arduino. An example of a voltage divider would look something like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

Remember, the formula for a voltage divider (should you have forgotten or don't know) is \$V_{Out}=\frac{R_2 V_{}in}{R_1+R_2}\$. It's a good idea to use larger resistors so that you can keep your current draw to a minimum.