Abstract: A core logic chip set in a computer system provides a bridge between processor host and memory buses and a plurality of peripheral component interconnect ("PCI") buses capable of operating at 66 MHz. Each of the plurality of PCI buses have the same logical bus number. The core logic chip set has an arbiter having Request ("REQ") and Grant ("GNT") signal lines for each PCI device connected to the plurality of PCI physical buses. Each of the plurality of PCI buses has its own read and write queues to provide transaction concurrency of PCI devices on different ones of the plurality of PCI buses when the transaction addresses are not the same or are M byte aligned. Upper and lower memory address range registers store upper and lower memory addresses associated with each PCI device. Whenever a transaction occurs, the transaction address is compared with the stored range of memory addresses. If a match between addresses is found then strong ordering is used.