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Abstract : |
ABSTRACT The problem of performing multtphcaUon of n-bit binary numbers on a chip is considered Let A denote the ch~p area and T the time reqmred to perform mult~phcation. By using a model of computation which is a realistic approx~mauon to current and anucipated LSI or VLSI technology, ~t is shown that A T 2. for all a ~ [0, 1], where A0 and To are posmve constants which depend on the technology but are mdependent of n. The exponent 1 + a is the best possible A consequence of this result is that binary multiphcatlon is "harder " than binary addmon More precisely, ff(AT2~)M(n) and (AT2~)A(n) denote the mmimum area-time complexity for n-b~t binary multiphcauon and addmon, respectively, then (AT2~)M(n) _ 1 f~(nl-a) for 0 _< a--< na for ~<a_<l for>, ( = fi(nl/2) for all a _> 0)., |
