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.