Computers are literally magic.
No, really. There's a few power crystals feeding energy into an array of memory crystals, which transfer information to and from a control crystal, which uses a limited sort of intelligence to tell all the other crystals what to do. There's one physically large array of crystals that show the user what the apparatus is doing, and a few crystals that send and receive information from other assemblages of crystals that act as a way for a user to control the system.