# Dimensioning a “NOT” gate with a bipolar NPN transistor

With the schematic below I am to determine a "NOT" gate the value of Rb to which the circuit acts as such, knowing that the voltages given for the logic levels are: $$0\to V\in[-0.3,0.9]$$ $$1\to V\in[2.5,5]$$

Now here's the problem: This is really new to me and I don't know how to even start. What I know is that a "NOT" gate gives a 0 if a 1 in given and vice-versa. But how should the transistor work? Should we get it to work in the linear regime, or in the saturation and cut off mode? Do I need to get a way for the input not to be anywhere between the logic level's voltage intervals, or not? And why is it an interval (In the real world I understand why, but in an idealized circuit is it really necessary?)?