All multi-functional displays in modern avionics are just computers. Typically, they are only responsible for presentation of the supplied information, but may do some processing: for example, display certain alerts in the right conditions. Also, they manage some of the
user pilot input and mode switching.
G1000 PFD diagnostics page
Nearly all the data comes in on digital bus(es), in aviation most commonly ARINC 429 or even Ethernet with a custom protocol.
Bare sensors either have a dedicated microcontroller that converts the readings to a digital format, or are connected to a dedicated processing unit (also a specialised computer), such as ADC (Air Data Computer) which collects and processes all the air-related data (airspeed, altitude, temperature, etc.)
Even then, typically, this semi-processed data don't go to displays directly. All the sensor data are collected by a sort of integration unit (e.g. GIA for Garmin systems), which does most of the processing and decision making. Then, the necessary information is relayed to the displays.