Small fan-in is beautiful

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The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions; and (2) another one for implementing certain subclasses of Boolean functions. Because VLSI implementations do not cope well with highly interconnected nets -- the area of a chip grows with the cube of the fan-in -- this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Horne and Hush valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimal solutions are obtained ... continued below

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9 p.

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Beiu, V. & Makaruk, H.E. September 1, 1997.

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Description

The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions; and (2) another one for implementing certain subclasses of Boolean functions. Because VLSI implementations do not cope well with highly interconnected nets -- the area of a chip grows with the cube of the fan-in -- this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Horne and Hush valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimal solutions are obtained for small constant fan-ins for both constructions, while relative minimum size solutions can be obtained for fan-ins strictly lower that linear. These results are in agreement with similar ones proving that for small constant fan-ins ({Delta} = 6...9) there exist VLSI-optimal (i.e., minimizing AT{sup 2}) solutions, while there are similar small constants relating to the capacity of processing information.

Physical Description

9 p.

Notes

OSTI as DE98000277

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  • IEEE world congress on computational intelligence, Anchorage, AK (United States), 5-9 May 1998

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  • Other: DE98000277
  • Report No.: LA-UR--97-3493
  • Report No.: CONF-980538--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 658318
  • Archival Resource Key: ark:/67531/metadc702073

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  • September 1, 1997

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  • Sept. 12, 2015, 6:31 a.m.

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  • May 5, 2016, 7:20 p.m.

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Beiu, V. & Makaruk, H.E. Small fan-in is beautiful, article, September 1, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc702073/: accessed August 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.