How to understand the transistor working in the saturation zone in the monolithic computer application

The standard for determining if the transistor is entering the saturation zone is ibxβ> Ic (max), because the analog circuit book in college was written on the condition that the NPN transistor is in the saturated zone is ube>0 ubc>0, but in single-chip microcomputer applications, the general collector is connected to VCC via a resistor, So the base of the voltage can not be higher than the collector, so I think it is also possible to understand that the IB increases, IC = Ibxβ also with the increase, if the IB increases to a certain value, the Ic does not increase with the IB, the transistor enters the saturation zone such as

Calculate the R37 R38 to make the transistor work in the saturated zone.

When the transistor working in the saturation zone, the saturation pipe pressure drop uces is very small, the general silicon transistor uces<0.4v, where I ignore it, then Ic (max) = 5v/r38 (r38=2k) =2.5ma, general transistor β=100, then Ib = 2.5ma/ 25uA allows the base current IB > 25uA transistor to work in the saturation zone. V (Trig) =3.3v vbes = 0.7V so r37≤ (3.3-0.7)/25ua≈100k take r37=1k, of course, R37 can not be too small, if too small to cause the base current is too large, it is possible to burn single-chip microcomputer or transistor.

How to understand the transistor working in the saturation zone in the monolithic computer application