Methods and apparatuses relating to memory compression and decompression are described, including a memory controller and methods for memory compression utilizing a hardware compression engine and a dictionary to indicate a zero value, full match, partial match, or no match. When indices for multiple sections are the same, an entry in the dictionary may be updated with the value of the section that is most recent, in the same order as in the block of data. In one embodiment, a hardware compression engine is to determine when each section of a plurality of sections of a block of data is a zero value, a full match or a partial match to an entry in a dictionary, or a no match to any entry in the dictionary, encode a tag for each section to indicate the one of the zero value, the full match, the partial match, and the no match, encode a literal when the section is the no match, an index to the entry in the dictionary when the section is the full match, and an index to the entry in the dictionary and non-matching bits when the section is the partial match, and update an entry in the dictionary with a value of a section when the section is the no match, wherein tags for the plurality of sections are to be output from the hardware compression engine in a single field, literals for the plurality of sections are to be output from the hardware compression engine in a single field, indexes for the plurality of sections are to be output from the hardware compression engine in a single field, and non-matching bits for the plurality of sections are to be output from the hardware compression engine in a single field. A hash value may be generated for each of a plurality of sections of a block of data to use as an index in a dictionary.