I am designing a digital output circuit.
I got confused about the position of the current limiting resistor of the transistor.
I would like know where it should be. (After or before the pull up resistor.)
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In your circuit, U23 is not a source of current into the Q25 base; it works by shunting base current away from the transistor. The base current is supplied solely by R110, so it's value should be calculated to deliver the current required to saturate the transistor.
In fact, R109 should be removed because it hurts the circuit. When U23 is on, R109 and R110 form a voltage divider, so the Q25 base voltage never is below (0.46 V + U23 Vcesat). This is not low enough to guarantee that Q25 turns completely off. Assuming Q25 has a nominal gain of 100, it takes only 50 uA of base current to drive it into light saturation.