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There is considerable interest at present in the design of asynchronous systems based on the use of self-timing components for arithmetic and other operations. Amongst the advantages claimed for asynchronous design are ease of design, high speed, low power, and device speed independence. An often quoted example of the speed improvement possible from self-timed hardware is parallel binary addition, where the carry signals in the worst case must propagate through n stages before the sum can be guaranteed correct. In practice, however, it is not possible to achieve significant speed advantage from the method, and this paper shows that asynchronous adders only give a performance improvement over more conventional hardware in very limited conditions, where the size and regularity of the layout are at a premium.