Completion of the Mission: Countdown quest requires a total of 15 undamaged mainframe cores. These can be obtained in one of two ways: by collecting damaged mainframe cores from the computer consoles in the lower level of Site Alpha, Site Bravo, and Site Charlie, and then repairing them at a Tinker's workbench. Alternatively, a small number of undamaged cores can be found scattered in the boxes and shelves that are present within the silos.
A damaged mainframe core can be repaired for use in the Mission: Countdown quest:
Mainframe core (1)