Abstract

Position-coded modulo m lookup tables (LUTs) with gate complexities equal to m2, 2m, and 4m are discussed. The design of practical miniaturized LUTs is described along with results obtained from a prototype 7 × 7 laser diode LUT. A factored m2 LUT technique that achieves large dynamic range is presented. Several LUT performance issues are also discussed.

© 1988 Optical Society of America

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References

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  1. N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).
  2. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, “Optical Computation Using Residue Arithmetic,” Appl. Opt. 18, 149 (1979).
    [CrossRef] [PubMed]
  3. A. Tai, I. Cindrich, J. R. Fienup, C. C. Aleksoff, “Optical Residue Arithmetic Computer with Programmable Computation Modules,” Appl. Opt. 18, 2812 (1979).
    [CrossRef] [PubMed]
  4. D. D. Miller, J. N. Polky, “A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits,” IEEE Trans. Comput. C-32, 1013 (1983).
    [CrossRef]
  5. T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
    [CrossRef]
  6. D. Psaltis, D. Casasent, “Optical Residue Arithmetic: A Correlation Approach,” Appl. Opt. 18, 163 (1979).
    [CrossRef] [PubMed]
  7. S. F. Habiby, S. A. Collins, “Design of an Optical Residue Arithmetic Matrix Vector Multiplier Using Holographic Table Lookup,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper TuD4.
  8. P. R. Beaudet, A. P. Goutzoulis, E. C. Malarkey, J. C. Bradley, “Residue Arithmetic Techniques for Optical Processing of Adaptive Phased Array Radars,” Appl. Opt. 25, 3097 (1986).
    [CrossRef] [PubMed]
  9. A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype Position-Coded Residue Look-Up Table Using Laser Diodes,” Opt. Commun. 61, 302 (1987).
    [CrossRef]
  10. C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.
  11. A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.
  12. P. R. Beaudet, “Optical Residue Arithmetic Computer,” Patent Disclosure AA86-008, Westinghouse Elec. Corp. (1985).
  13. D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
    [CrossRef]
  14. A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).
  15. E. C. Malarkey, P. R. Beaudet, J. C. Bradley, J. L. Davis, “Factored Look-Up Tables for Optical Residue Number System (RNS) Computations,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), poster paper.
  16. A. P. Goutzoulis, “Complexity of Residue Position-Coded Lookup Table Array Processors,” Appl. Opt. 26, 4823 (1987).
    [CrossRef] [PubMed]
  17. H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.
  18. W. R. Iversen, “A Faster GaAs Chip Nears Production,” Electronics36 (16Apr.1987).
  19. H. K. Chung, D. Arch, K. Betz, Honeywell Physical Sciences Center, Bloomington, MN; private communication.
  20. D. J. Schwab, Mayo Foundation, Special Purpose Processor Development Group, Rochester, MN; private communication.
  21. F. S. Lee et al., “A High Speed LSI GaAs 8 × 8 Bit Parallel Multiplier,” IEEE J. Solid State Circ. SC-17, 638 (1982).
    [CrossRef]
  22. M. Driver, M. Sopira, Westinghouse R&D Center, Pittsburgh, PA; private communication.
  23. A. Yariv, “Quantum-Well Lasers and Optoelectronics,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1987), paper WC1.

1987

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype Position-Coded Residue Look-Up Table Using Laser Diodes,” Opt. Commun. 61, 302 (1987).
[CrossRef]

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

W. R. Iversen, “A Faster GaAs Chip Nears Production,” Electronics36 (16Apr.1987).

A. P. Goutzoulis, “Complexity of Residue Position-Coded Lookup Table Array Processors,” Appl. Opt. 26, 4823 (1987).
[CrossRef] [PubMed]

1986

1985

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

1984

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

1983

D. D. Miller, J. N. Polky, “A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits,” IEEE Trans. Comput. C-32, 1013 (1983).
[CrossRef]

1982

F. S. Lee et al., “A High Speed LSI GaAs 8 × 8 Bit Parallel Multiplier,” IEEE J. Solid State Circ. SC-17, 638 (1982).
[CrossRef]

1979

Aleksoff, C. C.

Arch, D.

H. K. Chung, D. Arch, K. Betz, Honeywell Physical Sciences Center, Bloomington, MN; private communication.

Beaudet, P. R.

P. R. Beaudet, A. P. Goutzoulis, E. C. Malarkey, J. C. Bradley, “Residue Arithmetic Techniques for Optical Processing of Adaptive Phased Array Radars,” Appl. Opt. 25, 3097 (1986).
[CrossRef] [PubMed]

E. C. Malarkey, P. R. Beaudet, J. C. Bradley, J. L. Davis, “Factored Look-Up Tables for Optical Residue Number System (RNS) Computations,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), poster paper.

P. R. Beaudet, “Optical Residue Arithmetic Computer,” Patent Disclosure AA86-008, Westinghouse Elec. Corp. (1985).

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.

Betz, K.

H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.

H. K. Chung, D. Arch, K. Betz, Honeywell Physical Sciences Center, Bloomington, MN; private communication.

Bradley, J. C.

P. R. Beaudet, A. P. Goutzoulis, E. C. Malarkey, J. C. Bradley, “Residue Arithmetic Techniques for Optical Processing of Adaptive Phased Array Radars,” Appl. Opt. 25, 3097 (1986).
[CrossRef] [PubMed]

E. C. Malarkey, P. R. Beaudet, J. C. Bradley, J. L. Davis, “Factored Look-Up Tables for Optical Residue Number System (RNS) Computations,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), poster paper.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.

Burrus, C. A.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Capps, C.

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

Casasent, D.

Chemla, D. S.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Chung, H. K.

H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.

H. K. Chung, D. Arch, K. Betz, Honeywell Physical Sciences Center, Bloomington, MN; private communication.

Cindrich, I.

Collins, S. A.

S. F. Habiby, S. A. Collins, “Design of an Optical Residue Arithmetic Matrix Vector Multiplier Using Holographic Table Lookup,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper TuD4.

Damen, T. C.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Davies, D. K.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype Position-Coded Residue Look-Up Table Using Laser Diodes,” Opt. Commun. 61, 302 (1987).
[CrossRef]

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.

Davis, J. L.

E. C. Malarkey, P. R. Beaudet, J. C. Bradley, J. L. Davis, “Factored Look-Up Tables for Optical Residue Number System (RNS) Computations,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), poster paper.

Driver, M.

M. Driver, M. Sopira, Westinghouse R&D Center, Pittsburgh, PA; private communication.

Falk, R.

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

Fienup, J. R.

Gaylord, T. K.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Goodman, J. W.

Gossard, A. C.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Goutzoulis, A. P.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype Position-Coded Residue Look-Up Table Using Laser Diodes,” Opt. Commun. 61, 302 (1987).
[CrossRef]

A. P. Goutzoulis, “Complexity of Residue Position-Coded Lookup Table Array Processors,” Appl. Opt. 26, 4823 (1987).
[CrossRef] [PubMed]

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

P. R. Beaudet, A. P. Goutzoulis, E. C. Malarkey, J. C. Bradley, “Residue Arithmetic Techniques for Optical Processing of Adaptive Phased Array Radars,” Appl. Opt. 25, 3097 (1986).
[CrossRef] [PubMed]

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.

Guest, C. C.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Habiby, S. F.

S. F. Habiby, S. A. Collins, “Design of an Optical Residue Arithmetic Matrix Vector Multiplier Using Holographic Table Lookup,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper TuD4.

Houk, T.

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

Huang, A.

Ishihara, S.

Iversen, W. R.

W. R. Iversen, “A Faster GaAs Chip Nears Production,” Electronics36 (16Apr.1987).

Lee, F. S.

F. S. Lee et al., “A High Speed LSI GaAs 8 × 8 Bit Parallel Multiplier,” IEEE J. Solid State Circ. SC-17, 638 (1982).
[CrossRef]

Lee, G. V.

H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.

Malarkey, E. C.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype Position-Coded Residue Look-Up Table Using Laser Diodes,” Opt. Commun. 61, 302 (1987).
[CrossRef]

P. R. Beaudet, A. P. Goutzoulis, E. C. Malarkey, J. C. Bradley, “Residue Arithmetic Techniques for Optical Processing of Adaptive Phased Array Radars,” Appl. Opt. 25, 3097 (1986).
[CrossRef] [PubMed]

E. C. Malarkey, P. R. Beaudet, J. C. Bradley, J. L. Davis, “Factored Look-Up Tables for Optical Residue Number System (RNS) Computations,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), poster paper.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.

Miller, D. A.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Miller, D. D.

D. D. Miller, J. N. Polky, “A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits,” IEEE Trans. Comput. C-32, 1013 (1983).
[CrossRef]

Mirsalehi, M. M.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Polky, J. N.

D. D. Miller, J. N. Polky, “A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits,” IEEE Trans. Comput. C-32, 1013 (1983).
[CrossRef]

Psaltis, D.

Schwab, D. J.

D. J. Schwab, Mayo Foundation, Special Purpose Processor Development Group, Rochester, MN; private communication.

Sopira, M.

M. Driver, M. Sopira, Westinghouse R&D Center, Pittsburgh, PA; private communication.

Szabo, N. S.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Tai, A.

Tan, K. L.

H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.

Tanaka, R. I.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Tsunoda, Y.

Void, P. J.

H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.

Wiegmann, W.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Wood, T. H.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Yariv, A.

A. Yariv, “Quantum-Well Lasers and Optoelectronics,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1987), paper WC1.

Appl. Opt.

Appl. Phys. Lett.

D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “Novel Hybrid Optically Bistable Switch: The Quantum Well Self-Electro-Optic Effect Device,” Appl. Phys. Lett. 45, 13 (1984).
[CrossRef]

Electronics

W. R. Iversen, “A Faster GaAs Chip Nears Production,” Electronics36 (16Apr.1987).

IEEE J. Solid State Circ.

F. S. Lee et al., “A High Speed LSI GaAs 8 × 8 Bit Parallel Multiplier,” IEEE J. Solid State Circ. SC-17, 638 (1982).
[CrossRef]

IEEE Trans. Comput.

D. D. Miller, J. N. Polky, “A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits,” IEEE Trans. Comput. C-32, 1013 (1983).
[CrossRef]

Opt. Commun.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype Position-Coded Residue Look-Up Table Using Laser Diodes,” Opt. Commun. 61, 302 (1987).
[CrossRef]

Opt. Eng.

T. K. Gaylord, M. M. Mirsalehi, C. C. Guest, “Optical Digital Truth Table Look-Up Processing,” Opt. Eng. 24, 48 (1985).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

Other

E. C. Malarkey, P. R. Beaudet, J. C. Bradley, J. L. Davis, “Factored Look-Up Tables for Optical Residue Number System (RNS) Computations,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), poster paper.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, J. C. Bradley, P. R. Beaudet, “Residue Position-Coded Look-Up Table Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD3.

P. R. Beaudet, “Optical Residue Arithmetic Computer,” Patent Disclosure AA86-008, Westinghouse Elec. Corp. (1985).

H. K. Chung, G. V. Lee, K. L. Tan, K. Betz, P. J. Void, “High Speed and Ultra-Low Power GaAs MESFET 5 × 5 Multipliers,” in GaAs IC Symposium Technical Digest, Grenelefe, FL (1986), p. 15.

H. K. Chung, D. Arch, K. Betz, Honeywell Physical Sciences Center, Bloomington, MN; private communication.

D. J. Schwab, Mayo Foundation, Special Purpose Processor Development Group, Rochester, MN; private communication.

M. Driver, M. Sopira, Westinghouse R&D Center, Pittsburgh, PA; private communication.

A. Yariv, “Quantum-Well Lasers and Optoelectronics,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1987), paper WC1.

S. F. Habiby, S. A. Collins, “Design of an Optical Residue Arithmetic Matrix Vector Multiplier Using Holographic Table Lookup,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), paper TuD4.

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Figures (9)

Fig. 1
Fig. 1

Lookup tables for (a) multiplication and (b) addition in modulo 5 residue arithmetic.

Fig. 2
Fig. 2

m i 2 type LED or LD residue lookup table.

Fig. 3
Fig. 3

2m i -type LED or LD residue lookup table.

Fig. 4
Fig. 4

Optical arrangement for producing the rows (or columns) of a 4 m i type residue lookup table.

Fig. 5
Fig. 5

IEG 7 × 7 laser diode prototype LUT.

Fig. 6
Fig. 6

Output intensity pattern LUT geometry (a) when (1,1) (b), (4,5) (c), and (7,7) (d) rows, columns are excited.

Fig. 7
Fig. 7

3 × 3 miniaturized LED IEG LUT.

Fig. 8
Fig. 8

Development and implementation of factored LUTs for (a) direct and (b) logarithmic multiplication.

Fig. 9
Fig. 9

Gate complexity as a function of array dimension N for the four LUT approaches.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

( a + b ) = ( Γ α + Γ β ) m = Γ α [ 1 + Γ ( β α ) m 1 ] m Γ α Γ γ = Γ ( α + γ ) m 1 ( c ) m .
4 i m i 2 ,

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