Submitted

Number representations in computers are typically chosen for reasons of range and precision. Little consideration has been given to the impact of a representation on the complexity of the operations that must manipulate it or to the distribution of "weight " over the bits of a format. While some integer representations have been analyzed with respect to a particular implemen-tation technology, we instead applied abstract complexity theory to the Boolean functions corresponding to operations (addition and multiplication) upon a wide variety of formats. * Since the analysis provides information about the "ease " with which particular bits are handled, tradeoffs between the uses of the bits (between range and precision of a floating-point format, for example) can be more informed. Initial results confirmed conventional wisdom: A twos complement format has a low complexity and a RNS format can provide vastly improved multiplication implementations. We found that testing for invalid inputs was a major contribution to operations using some representations. The project also involved optimization of the analysis, implemented as a ’C ’ program running on VAX and Cray computers. Though the implementation remains limited by computing resources, this application of abstract complexity theory provides a ne