Here is a Web site by a guy who designed working versions of all the basic logic gates, that is the NOT, OR, NOR, AND, and NAND gates, with Lego blocks.
His Legobased XOR gate is a single gate in its own right, i.e., not a composition of ANDs, ORs and NOTs. Using two NAND gates he created a NAND gate latch or flip-flop. http://goldfish.ikaruga.co.uk/logic.html