Methods and apparatus for Exclusive OR (XOR) programming of a memory device include a program internal to a device calculates parity or other values using an XOR Program Rule. In some embodiments, the program generates and stores a parity result directly in the memory device itself without intervention by an external controller. A method of parity generation in a memory device comprises executing an internal self-accumulating parity program, wherein the program accumulates a parity sum by superimposing newly accumulated parity information over previously stored parity information in the auxiliary memory system. In a stand-alone device embodiment, a new command “XOR program” is received with address and input data parameters causing stored data to be read at the input address and an XOR operation of the read data and new input data is performed. The results of the computation are written into memory.