In a computer system having a plurality of processors and processes, a semaphore architecture for communication with and between the processes in order to effects coordination and cooperation between processes. The invention is implemented in firmware and software, and divides the work of an entire semaphore operation such that the simple part of the P and V operations (which deliver and pick-up signals to and from the processes, respectively) is done by the firmware; whereas the difficult work of the P or V operation is done by software. Thus the improved architecture increases the speed of the system by the use of firmware and increases the flexibility of the computer system by utilizing software to change functionality.