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We present a nanometer-scale computation scheme in which all of the devices and interconnects required for the one-time computation of an arbitrary logic function are implemented by atomically-precise arrangements of molecules bound to a surface. The motion of one CO molecule on a Cu (111) surface causes a nearby molecule to hop to a new site, which in turn moves another molecule, and so on in a cascade of motion similar to a row of toppling dominoes. This cascade communicates one bit of information across the surface. Logic gates and other devices are implemented by engineered arrangements of molecules at the intersections of these cascades. We use a low-temperature scanning tunnelling microscope to assemble and demonstrate a 3-input sorter that uses several AND gates and OR gates, and the crossover and fan-out units needed to connect them.