begingroup$ Yes. In fact, any logical operation can be built from the NAND operator, where A NAND B = NOT(A AND B) See for instance http://en.wikipedia.org/wiki/NAND_logic, which gives A XOR B = (A NAND (A NAND B)) NAND (B NAND (A NAND B)) Digression: There is a story about certain military devices being designed using only NAND gates, so that only one part needs to be certified, stocked as spares, etc.