Abstract: A priority system in which eight priority request signals from eight associated requestors R7-R.phi. may simultaneously request access to an associated memory unit and may be honored in one of several priority modes. In a first mode the requestors R7-R.phi. are honored pre-emptively or in a numerically descending ordered manner in which priority selection is from the highest ordered priority requestor R7 first to the lowest ordered priority requestor R.phi. last. In a second mode the requestors R7-R.phi. are functionally divided into 4 groups of 2 requestors per group in which the priority request signals from the 4 groups 4, 3, 2, 1 of requestors may be selected pre-emptively, e.g., groups 4; 3; 2; 1 of requestors R7, R6; R5, R4; R3, R2; R1, R.phi. respectively, are honored in a numerically descending ordered manner in which the priority selection is from the highest priority group 4 first to the lowest priority group 1 last and in which priority between requestors within a group, e.g.