At a very basic level, primary flight displays take data from sensors, do calculations, and display the results on a screen. Of course, because they are digital computers, the input must be digital, at least inside the processor. However, the values being measured, such as air pressure, airspeed, etc., are fundamentally analog, so there must be analog sensors involved. At what point is the analog data from the sensors converted to digital data for the computer?
Glass cockpits are modular systems, and not all of them are exactly the same. But many/most include a module called an Air Data Computer (ADC) which performs the digitalization function for the parameters you mentioned (air pressure [= altitude] and airspeed). This is a self-contained module installed in the aircraft. It will have pneumatic connections for the actual sensors on the airframe, and some form of digital output, like an ARINC 429 data bus connected to other modules in the system like the displays. Sometimes the digital data first goes through another module like an I/O concentrator before it reaches the displays.
For a concrete example, this particular Garmin G1000 system digitizes air data using a GDC 74A air data computer:
The installation manual for the GDC 74A shows its pneumatic connections:
Other modules like Attitude/Heading Reference Systems (AHRS) perform similar digitization and filtering functions for signals from sources like magnetometers and accelerometers for aircraft orientation or rates. Many systems have several other types of modules, or in-sensor digitization, for radio altimeters, flight control servos, etc. etc.
On smaller aircraft, the conversion is done within the Air Data Computer (see TypeIA's answer). This makes replacing older steam gauges with a glass cockpit relatively simple because you just send the existing pitot/static lines to the ADC instead of the instruments directly.
On lager airliners, which were designed with a glass cockpit from the beginning, you typically want to do the conversion to digital data earlier. This avoids having several long pitot and static lines going through the entire aircraft, which saves weight. For example, on the Airbus A320 only the standby instruments have direct pitot and static lines. Everything else is converted to digital data in Air Data Modules earlier:
The system includes [...] eight ADMs (Air Data Modules) which convert pneumatic data from PITOT and STAT probes into numerical data for the ADIRUs. [...]
(Airbus A320 FCOM - Navigation - ADIRS)
I think on newer A320 variants, which use the digital Integrated Standby Instrument System (ISIS), they also removed these pitot and static lines and use the ADM data directly, but I couldn't find a reference to confirm this.