Complex sentence: Electronics were expensive, so it was generally assumed that each home would have only one multitasking computer for the entire family to use in a timesharing arrangement, with interfaces to the various devices it was expected to control.
Split into simpler sentences: Electronics were expensive, so it was generally assumed that each home would have only one multitasking computer for the entire family to use. Home control would be performed in a timesharing arrangement, with interfaces to the various devices it was expected to control.