Abstract

The use of the twos complement binary representation in performing matrix–matrix multiplication using an optical engagement array architecture is presented. Twos complement arithmetic offers a convenient means for handling bipolar numbers, avoids the need for matrix partitioning when the matrices are real, and offers a means to improve accuracy over conventional optical analog techniques.

© 1983 Optical Society of America

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References

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  1. R. A. Athale, W. C. Collins, P. D. Stilwell, Appl. Opt. 22, 368 (1983).
    [CrossRef] [PubMed]
  2. W. C. Collins, R. A. Athale, P. D. Stilwell, Proc. Soc. Photo-Opt. Instrum. Eng. 352, (1983).
  3. R. A. Athale, W. C. Collins, Appl. Opt. 21, 2089 (1982).
    [CrossRef] [PubMed]
  4. A. Tarasevich, N. Zepkin, W. T. Rhodes, “Matrix Vector Multiplier with Time-Varying Single Dimensional Spatial Light Modulators,” Optical Information Processing for Aerospace Applications, NASA Conference Publication 2207 (NTIS, Springfield, Va., 1981).
  5. H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, G. Tacconi, Ed. (Reidel, Dordrecht, 1977), Part 2.
  6. D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).
  7. R. P. Bocker, H. J. Caulfield, K. Bromley, Appl. Opt. 22, 804 (1983).
    [CrossRef] [PubMed]
  8. R. P. Bocker, H. J. Caulfield, K. Bromley, Proc. Soc. Photo-Opt. Instrum. Eng. 388, (1983).
  9. D. E. Johnson, J. L. Hilburn, P. M. Julich, Digital Circuits and Microcomputers (Prentice-Hall, Englewood Cliffs, N.J., 1979), pp. 216–220.
  10. H. T. Kung, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 76 (1980).
  11. J. M. Speiser, H. J. Whitehouse, Proc. Soc. Photo-Opt. Instrum. Eng. 298, 2 (1981).

1983

R. A. Athale, W. C. Collins, P. D. Stilwell, Appl. Opt. 22, 368 (1983).
[CrossRef] [PubMed]

W. C. Collins, R. A. Athale, P. D. Stilwell, Proc. Soc. Photo-Opt. Instrum. Eng. 352, (1983).

R. P. Bocker, H. J. Caulfield, K. Bromley, Appl. Opt. 22, 804 (1983).
[CrossRef] [PubMed]

R. P. Bocker, H. J. Caulfield, K. Bromley, Proc. Soc. Photo-Opt. Instrum. Eng. 388, (1983).

1982

1981

J. M. Speiser, H. J. Whitehouse, Proc. Soc. Photo-Opt. Instrum. Eng. 298, 2 (1981).

1980

H. T. Kung, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 76 (1980).

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Athale, R. A.

Bocker, R. P.

R. P. Bocker, H. J. Caulfield, K. Bromley, Appl. Opt. 22, 804 (1983).
[CrossRef] [PubMed]

R. P. Bocker, H. J. Caulfield, K. Bromley, Proc. Soc. Photo-Opt. Instrum. Eng. 388, (1983).

Bromley, K.

R. P. Bocker, H. J. Caulfield, K. Bromley, Proc. Soc. Photo-Opt. Instrum. Eng. 388, (1983).

R. P. Bocker, H. J. Caulfield, K. Bromley, Appl. Opt. 22, 804 (1983).
[CrossRef] [PubMed]

Carlotto, M.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Casasent, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Caulfield, H. J.

R. P. Bocker, H. J. Caulfield, K. Bromley, Proc. Soc. Photo-Opt. Instrum. Eng. 388, (1983).

R. P. Bocker, H. J. Caulfield, K. Bromley, Appl. Opt. 22, 804 (1983).
[CrossRef] [PubMed]

Collins, W. C.

Hilburn, J. L.

D. E. Johnson, J. L. Hilburn, P. M. Julich, Digital Circuits and Microcomputers (Prentice-Hall, Englewood Cliffs, N.J., 1979), pp. 216–220.

Johnson, D. E.

D. E. Johnson, J. L. Hilburn, P. M. Julich, Digital Circuits and Microcomputers (Prentice-Hall, Englewood Cliffs, N.J., 1979), pp. 216–220.

Julich, P. M.

D. E. Johnson, J. L. Hilburn, P. M. Julich, Digital Circuits and Microcomputers (Prentice-Hall, Englewood Cliffs, N.J., 1979), pp. 216–220.

Kung, H. T.

H. T. Kung, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 76 (1980).

Neft, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Psaltis, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Rhodes, W. T.

A. Tarasevich, N. Zepkin, W. T. Rhodes, “Matrix Vector Multiplier with Time-Varying Single Dimensional Spatial Light Modulators,” Optical Information Processing for Aerospace Applications, NASA Conference Publication 2207 (NTIS, Springfield, Va., 1981).

Speiser, J. M.

J. M. Speiser, H. J. Whitehouse, Proc. Soc. Photo-Opt. Instrum. Eng. 298, 2 (1981).

H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, G. Tacconi, Ed. (Reidel, Dordrecht, 1977), Part 2.

Stilwell, P. D.

R. A. Athale, W. C. Collins, P. D. Stilwell, Appl. Opt. 22, 368 (1983).
[CrossRef] [PubMed]

W. C. Collins, R. A. Athale, P. D. Stilwell, Proc. Soc. Photo-Opt. Instrum. Eng. 352, (1983).

Tarasevich, A.

A. Tarasevich, N. Zepkin, W. T. Rhodes, “Matrix Vector Multiplier with Time-Varying Single Dimensional Spatial Light Modulators,” Optical Information Processing for Aerospace Applications, NASA Conference Publication 2207 (NTIS, Springfield, Va., 1981).

Whitehouse, H. J.

J. M. Speiser, H. J. Whitehouse, Proc. Soc. Photo-Opt. Instrum. Eng. 298, 2 (1981).

H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, G. Tacconi, Ed. (Reidel, Dordrecht, 1977), Part 2.

Zepkin, N.

A. Tarasevich, N. Zepkin, W. T. Rhodes, “Matrix Vector Multiplier with Time-Varying Single Dimensional Spatial Light Modulators,” Optical Information Processing for Aerospace Applications, NASA Conference Publication 2207 (NTIS, Springfield, Va., 1981).

Appl. Opt.

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

R. P. Bocker, H. J. Caulfield, K. Bromley, Proc. Soc. Photo-Opt. Instrum. Eng. 388, (1983).

H. T. Kung, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 76 (1980).

J. M. Speiser, H. J. Whitehouse, Proc. Soc. Photo-Opt. Instrum. Eng. 298, 2 (1981).

W. C. Collins, R. A. Athale, P. D. Stilwell, Proc. Soc. Photo-Opt. Instrum. Eng. 352, (1983).

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, Proc. Soc. Photo-Opt. Instrum. Eng. 232, 151 (1980).

Other

A. Tarasevich, N. Zepkin, W. T. Rhodes, “Matrix Vector Multiplier with Time-Varying Single Dimensional Spatial Light Modulators,” Optical Information Processing for Aerospace Applications, NASA Conference Publication 2207 (NTIS, Springfield, Va., 1981).

H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, G. Tacconi, Ed. (Reidel, Dordrecht, 1977), Part 2.

D. E. Johnson, J. L. Hilburn, P. M. Julich, Digital Circuits and Microcomputers (Prentice-Hall, Englewood Cliffs, N.J., 1979), pp. 216–220.

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Figures (5)

Fig. 1
Fig. 1

Symbolic representation of the multiplication of two matrices using the engagement-array format.

Fig. 2
Fig. 2

Multiplication of two numbers in twos complement representation whose product is expressed in a mixed binary representation.

Fig. 3
Fig. 3

Example of the multiplication of two matrices using the engagement-array format (decimal representation).

Fig. 4
Fig. 4

Method for encoding the input matrix element information using the twos complement binary representation.

Fig. 5
Fig. 5

Example of the multiplication of two matrices using the engagement-array format (twos complement representation).

Equations (1)

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( - 2.00 + 3.50 - 0.50 + 0.50 + 1.50 + 1.00 - 1.50 + 2.00 + 0.00 ) A ( + 2.00 - 2.50 + 0.50 + 1.50 - 0.50 - 1.00 - 1.00 + 0.00 - 2.50 ) B = ( + 1.75 + 3.25 - 3.25 + 2.25 - 2.00 - 3.75 + 0.00 + 2.75 - 2.75 ) C .

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