Selecting bias resistor for thermistor

Rt is thermistor. Rb is bias resistor, which value I need to calculate. The temperature that I'm interested in is giving Rt resistance range of 4k...115k. What I want is to scale this to whole ADC resolution, which is 10 bit ie 0...1023. So when Rt = Rb ADC will convert it to 511. Not sure if it's possible, but ideally I would like to get 0 ADC reading when Rt = 4k and 1023 when Rt = 115k (or the other way).

Internally in MC I have lookup table, which will convert ADC value to temperature, according to curve described in thermistor datasheet.

My suggestion is to use digital thermometer. I have used Dallas DS18B20 using OneWire library. And I can say only the best about them - very precise and stable. And dead simple to use.

Arty:
My suggestion is to use digital thermometer. I have used Dallas DS18B20 using OneWire library. And I can say only the best about them - very precise and stable. And dead simple to use.

Unfortunately this is not an option due to many reasons.

ideally I would like to get 0 ADC reading when Rt = 4k and 1023 when Rt = 115k (or the other way).

Fortunately, that's not possible.

Well ... I'm afraid you cannot get the full 0-5v output using just the voltage divider. You can get only the half of it.. like 0-2.5v (using the same 4k as Rb). You should be using at least 10 volt power source to get full 0-5v ADC resolution ( 0.336V to 5V using the 4k Rb). Or 2.8k for the best resolution if you are using 12v power source ( 0.285v to 4.941). Please correct me if I'm wrong.