I think they'd be analog - they'd have to be practical size. Maybe this could offer an alternative path to miniaturization - a technological road not taken in our time line. Instead of making each switch/circuit tiny and including millions of them (as per modern digital technology), stick to huge switches/circuits, but make each one perform/store a range of functions & values.
Since this is the 1950s, ideally they'd also be powered by a lump of the fuel of tomorrow (plutonium), be made from shiny Aluminium, and have tail fins.