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The reference voltage depends on various factors: i) Type of circuit you want to build ii) Technology node iii) Interface logic....
That having said, your reference voltage for e.g. in the case of an Op-amp circuit should be a voltage which is used as a differential, which depending on the circuit design will provide the correct output.
In the case of technology node, the reference voltage for e.g. as the node size shrinks 65nm the supply could be 1.2V so you will have to have a reference voltage according to this node.
In the case of interfacing between different logic levels you could also use a reference voltage.
Most importantly the ground is also a reference voltage.
1.24V is the "golden" number for silicon-based voltage references.
As that is the bandgap voltage for Silicon, and hence the most accurate reference you can get.
All other reference voltages are derived from the bandgap voltage.
2.5V is about double of bandgap voltage.
In fact 0.6V is chosen for reference in many power management IC.
Sometimes, reference voltage is chosen according suitable resistor values for resistor divider.
bandgap voltages are essentially function of the technology node i.e. doping, channel length, gate width, material properties... So it is important to check it with teh technology node that the chip is designed.
"bandgap" references have only a coincidental relation to the material
Aside from the 1.23-ish, the rest of the values posed are just fitted to
applications - 2.048 for a mV/LSB nice round number on an A/D, logic
family nominal VCC/VDD, low enough reference that any presently existing
logic supply output can be made by a feedback divider, etc. Somebody
wanted it, somebody built it. Not much more to it than that.