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

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.

REFERENCES

• 1: D. Buell et.al. Splash2: FPGAs in a Custom Computing Machine. IEEE Coputer Science Press, 1996.
• 2: Uwe Meyer-Baese , Uwe Meyer Baese, Digital Signal Processing with Field Programmable Gate Arrays with Cdrom, Springer-Verlag New York, Inc., Secaucus, NJ, 2001
• 3: Varghese George and Jan M. Rabaey. Low Energy FPGA. Kluer Academic Publishers, 2001.
• 4: APEXII Programmable Logic Device Family Data Sheeet. Altera Corporation, 2000.
• 5: Scott Hauck , Thomas W. Fry , Matthew M. Hosler, High-performance carry chains for FPGA's, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, v.8 n.2, p.138-147, April 2000 [doi>10.1109/92.831434 ]
• 6: http://www.altera.co.jp.

INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.1 Types and Design Styles
          Subjects: Gate arrays

Additional Classification:
  B. Hardware
  B.5 REGISTER-TRANSFER-LEVEL IMPLEMENTATION
      B.5.1 Design
          Subjects: Memory design

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Analysis of algorithms

General Terms:
Algorithms, Design, Theory