Abstract: A memory accessing system for reading or writing consecutive addressable words is described for use in a set associative memory system. Two high speed buffer memories store words read in blocks from a slower main memory. One buffer stores even addressed words and the other stores odd addressed words. Each buffer memory has a tag memory associated with it for indicating data words stored in the buffer memories. A comparison circuit compares two addresses to be accessed to the tags and provides hit or miss signals for each address indicating residency or non-residency in the buffers. If both addressed words are resident, access to read or write the two consecutive data words is accomplished simultaneously. If either or both addressed words are not resident in the buffers, the main memory is accessed to acquire a block or blocks containing the missing addressed word or words. Consecutively addressed data words can occur within a block or across block boundary.