In my opinion, Lordac, you should become a lawyer, you already have the twists of translation.
First of all, TTL gates do not use output pull-up resistors, because this extends the turn-off time and increases power consumption.
In a normal gate, the high state is forced by the emitter follower and the low state by a transistor in the common emitter circuit that shorts the output to ground.
In open collector gates, the output stage has only the lower transistor, which means that it can force the output to be low.
The high state must be forced by external elements.
This system can control a display with a common anode and using a series resistor limiting the current flow.
R=(Ucc-Ucesat-Ud)/Id
Where
Ucc - supply voltage
Ucesat - gate output transistor saturation voltage (0.2V-0.4V)
Ud - forward voltage of the light-emitting diode (segment)
Id - diode (segment) current.
If we control in a multiplex system where we turn on N displays successively, the resistor must be N times smaller than the one obtained from the above formula to maintain the average value of the segment current equal to Id. However, you should remember about the protection that turns off the display when the sweep is stopped (without this, there will be a small boom and the currently lit display segments will fly.
When controlling high-voltage components, systems with increased output voltage should be used.
It should also be remembered that the total current drawn from the outputs of one system cannot exceed the maximum common-mode current and the power dissipated in the system cannot exceed its maximum power (the sum of the power dissipated in all output transistors < Pmax).