I don't know about Omron, but generally the process goes like this:
(Input)
Signal is received (4-20ma)
It is converted to a 1 to 5V signal.
This is then run through a AtoD converter. The most popular seem to be 12 bit, but you can get anything from 8 to 16 bit depending on the manufacturer. I will assume 12 bit for the rest of this analysis.
Once the conversion is complete, the value is placed in a register. This is generally a 16 bit register, giving you a value from 0000 to 0FFF (Hex).
This value is then used as the PLC process variable.
This is the basic process that all PLCs use, although each step can have its unique variations depending on the whims of the manufacturer and customer demands.
One popular variation is to convert the process variable into a floating point value. In that case, it is scaled between a minimum and maximum value. Example, you have a pressure input from 1 to 6 bar, with 1 bar = 4ma and 6 bar = 20ma.
You setup the scaling in your PLC to 0000 = 1 bar and 0FFF = 6 bar, and the conversion does the rest.
Hopefully this will give you a bit of a better insite into how it works.