Multiple instances of operating systems execute cooperatively in a single multiprocessor computer wherein all processors and resources are electrically connected together. The single physical machine with multiple physical processors and resources is subdivided by software into multiple partitions, each with the ability to run a distinct copy, or instance, of an operating system. At different times, different operating system instances may be loaded on a given partition. Resources, such as CPUs and memory, can be dynamically assigned to different partitions and used by instances of operating systems running within the machine by modifying the configuration. The partitions themselves can also be changed without rebooting the system by modifying the configuration tree. Each instance keeps track of the CPUs in the system and their respective operational statuses relative to the instance, such as compatibility with the instance, control by the instance, and availability to the instance for SMP processing. Using separate bitvectors for the different categories, a single bit in each bitvector may be used to represent the membership of a given CPU in that particular set, and therefore in the category represented by that set.