Folding of logic functions and its application to look up table compaction

  • Authors:
  • Shinji Kimura;Takashi Horiyama;Masaki Nakanishi;Hirotsugu Kajihara

  • Affiliations:
  • Waseda University, 2-2 Hibikino 808-0135, Japan;Kyoto University, Kyoto, Japan;Information Science, Nara Institute of Science and Technology, Takayama, Japan;Information Science, Nara Institute of Science and Technology, Takayama, Japan

  • Venue:
  • Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
  • Year:
  • 2002

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Abstract

The paper describes the folding method of logic functions to reduce the size of memories for keeping the functions. The folding is based on the relation of fractions of logic functions. We show that the fractions of the full adder function have the bit-wise NOT relation and the bit-wise OR relation, and that the memory size becomes half (8-bit). We propose a new 3--1 LUT with the folding mechanisms whcih can implement a full adder with one LUT. A fast carry propagation line is introduced for a multi-bit addition. The folding and fast carry propagation mechanisms are shown to be useful to implement other multi-bit operations and general 4 input functions without extra hardware resources. The paper shows the reduction of the area consumption when using our LUTs compared to the case using 4--1 LUTs on several benchmark circuits.