Abstract

Modified signed-digit (MSD) numbers offer convenient parallel addition and subtraction of bits. The parallel addition of any two MSD numbers, no matter what the values of their bits may be, requires only three bit-pattern transformations. To perform such transformations optically, however, MSD data must be represented in a form suitable for cascade connection. Proposed here is a new cascade-connective MSD optical processor. Adding principles are successfully demonstrated by using an optical threshold device array in addition to new computer-generated holograms that are adjusted to equalize the intensity of their diffracted light beams.

© 1992 Optical Society of America

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References

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  1. A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
    [CrossRef]
  2. B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).
  3. R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-signed-digit addition and subtraction using optical symbolic substitution,” Appl. Opt. 25, 2456–2457 (1986).
    [CrossRef] [PubMed]
  4. Y. Li, G. Eichmann, “Conditional symbolic modified signed-digit arithmetic using optical content-addressable memory logic elements,” Appl. Opt. 26, 2328–2333 (1987).
    [CrossRef] [PubMed]
  5. Y. Li, J. Zhu, G. Eichmann, “Optical on-the-fly conversion of a modified signed digit into two’s complement binary number representation,” Opt. Lett. 13, 294–296 (1988).
    [CrossRef] [PubMed]
  6. S. Mukhopadhyay, A. Basuray, A. K. Datta, “New coding scheme for addition and subtraction using the modified signed-digit number representation in optical computation,” Appl. Opt. 27, 1375–1376 (1988).
    [CrossRef] [PubMed]
  7. A. K. Cherri, M. A. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
    [CrossRef] [PubMed]
  8. A. A. S. Awwal, M. A. Karim, “Polarization-encoded optical shadow-casting: direct implementation of a carry-free adder,” Appl. Opt. 28, 785–790 (1989).
    [CrossRef] [PubMed]
  9. Y. Li, B. Ha, A. Kostrzewski, D. H. Kim, G. Eichmann, “Optical position-coded multiple-valued logic and arithmetic using liquid-crystal TVs and holograms,” Opt. Commun. 70, 379–383 (1989).
    [CrossRef]
  10. Y. Li, H. Kim, A. Kostrzewski, G. Eichmann, “Content-addressable-memory-based single-stage optical modified-signed-digit arithmetic,” Opt. Lett. 14, 1254–1256 (1989).
    [CrossRef] [PubMed]
  11. S. Kawai, Y. Kohga, “Modified signed-digit optical adder using computer-generated holograms,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 11B4.
  12. K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substitution,” Opt. Eng. 28, 364–372 (1989).
  13. A. K. Datta, A. Basuray, S. Mukhopadhyay, “Arithmetic operations in optical computations using a modified triary number system,” Opt. Lett. 14, 426–428 (1989).
    [CrossRef] [PubMed]
  14. S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.
  15. I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
    [CrossRef]
  16. K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
    [CrossRef]
  17. Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
    [CrossRef]
  18. N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.
  19. S. Kawai, Y. Tashiro, H. Ichinose, K. Kasahara, “Cascade connective optical parallel logic processor using electrophotonic devices,” Appl. Opt. 31, 178–185 (1992).
    [CrossRef] [PubMed]

1992 (1)

1990 (1)

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

1989 (6)

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

A. A. S. Awwal, M. A. Karim, “Polarization-encoded optical shadow-casting: direct implementation of a carry-free adder,” Appl. Opt. 28, 785–790 (1989).
[CrossRef] [PubMed]

Y. Li, B. Ha, A. Kostrzewski, D. H. Kim, G. Eichmann, “Optical position-coded multiple-valued logic and arithmetic using liquid-crystal TVs and holograms,” Opt. Commun. 70, 379–383 (1989).
[CrossRef]

Y. Li, H. Kim, A. Kostrzewski, G. Eichmann, “Content-addressable-memory-based single-stage optical modified-signed-digit arithmetic,” Opt. Lett. 14, 1254–1256 (1989).
[CrossRef] [PubMed]

K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substitution,” Opt. Eng. 28, 364–372 (1989).

A. K. Datta, A. Basuray, S. Mukhopadhyay, “Arithmetic operations in optical computations using a modified triary number system,” Opt. Lett. 14, 426–428 (1989).
[CrossRef] [PubMed]

1988 (4)

1987 (1)

1986 (2)

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-signed-digit addition and subtraction using optical symbolic substitution,” Appl. Opt. 25, 2456–2457 (1986).
[CrossRef] [PubMed]

1961 (1)

A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
[CrossRef]

Asada, S.

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

Avizienis, A.

A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
[CrossRef]

Awwal, A. A. S.

Basuray, A.

Bocker, R. P.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-signed-digit addition and subtraction using optical symbolic substitution,” Appl. Opt. 25, 2456–2457 (1986).
[CrossRef] [PubMed]

Cherri, A. K.

Datta, A. K.

Drake, B. L.

R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-signed-digit addition and subtraction using optical symbolic substitution,” Appl. Opt. 25, 2456–2457 (1986).
[CrossRef] [PubMed]

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

Eichmann, G.

Fujiwara, M.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Ha, B.

Y. Li, B. Ha, A. Kostrzewski, D. H. Kim, G. Eichmann, “Optical position-coded multiple-valued logic and arithmetic using liquid-crystal TVs and holograms,” Opt. Commun. 70, 379–383 (1989).
[CrossRef]

Hamao, H.

K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
[CrossRef]

Hamao, N.

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

Henderson, T. B.

Hwang, K.

K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substitution,” Opt. Eng. 28, 364–372 (1989).

Ichinose, H.

Karim, M. A.

Kasahara, K.

S. Kawai, Y. Tashiro, H. Ichinose, K. Kasahara, “Cascade connective optical parallel logic processor using electrophotonic devices,” Appl. Opt. 31, 178–185 (1992).
[CrossRef] [PubMed]

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
[CrossRef]

S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.

Kawai, S.

S. Kawai, Y. Tashiro, H. Ichinose, K. Kasahara, “Cascade connective optical parallel logic processor using electrophotonic devices,” Appl. Opt. 31, 178–185 (1992).
[CrossRef] [PubMed]

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

S. Kawai, Y. Kohga, “Modified signed-digit optical adder using computer-generated holograms,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 11B4.

Kim, D. H.

Y. Li, B. Ha, A. Kostrzewski, D. H. Kim, G. Eichmann, “Optical position-coded multiple-valued logic and arithmetic using liquid-crystal TVs and holograms,” Opt. Commun. 70, 379–383 (1989).
[CrossRef]

Kim, H.

Kobayashi, H.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Kohga, Y.

S. Kawai, Y. Kohga, “Modified signed-digit optical adder using computer-generated holograms,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 11B4.

Kostrzewski, A.

Y. Li, H. Kim, A. Kostrzewski, G. Eichmann, “Content-addressable-memory-based single-stage optical modified-signed-digit arithmetic,” Opt. Lett. 14, 1254–1256 (1989).
[CrossRef] [PubMed]

Y. Li, B. Ha, A. Kostrzewski, D. H. Kim, G. Eichmann, “Optical position-coded multiple-valued logic and arithmetic using liquid-crystal TVs and holograms,” Opt. Commun. 70, 379–383 (1989).
[CrossRef]

Kosuge, K.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Kubota, K.

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Lasher, M. E.

R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-signed-digit addition and subtraction using optical symbolic substitution,” Appl. Opt. 25, 2456–2457 (1986).
[CrossRef] [PubMed]

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

Li, Y.

Louri, A.

K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substitution,” Opt. Eng. 28, 364–372 (1989).

Miceli, W. J.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

Miyazaki, H.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Mukhopadhyay, S.

Nishida, N.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Ogura, I.

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.

Ohta, Y.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Ono, Y.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Patterson, R. H.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

Sakaguchi, M.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Shirakabe, K.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Sugama, S.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

Sugimoto, M.

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
[CrossRef]

Takado, N.

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

Tashiro, Y.

S. Kawai, Y. Tashiro, H. Ichinose, K. Kasahara, “Cascade connective optical parallel logic processor using electrophotonic devices,” Appl. Opt. 31, 178–185 (1992).
[CrossRef] [PubMed]

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
[CrossRef]

S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.

Yamada, K.

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.

Yanase, T.

K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
[CrossRef]

Zhu, J.

Appl. Opt. (6)

Appl. Phys. Lett. (3)

I. Ogura, Y. Tashiro, S. Kawai, K. Yamada, K. Kubota, K. Kasahara, “Reconfigurable optical interconnection using a two-dimensional vertical to surface transmission electrophotonic device array,” Appl. Phys. Lett. 57, 540–542 (1990).
[CrossRef]

K. Kasahara, Y. Tashiro, H. Hamao, M. Sugimoto, T. Yanase, “Double heterostructure optoelectronic switch as a dynamic memory with low-power consumption,” Appl. Phys. Lett. 52, 679–681 (1988).
[CrossRef]

Y. Tashiro, N. Hamao, M. Sugimoto, N. Takado, S. Asada, K. Kasahara, “Vertical to surface transmission electrophotonic device with selectable output light channels,” Appl. Phys. Lett. 54, 329–331 (1989).
[CrossRef]

IRE Trans. Electron. Comput. (1)

A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
[CrossRef]

Opt. Commun. (1)

Y. Li, B. Ha, A. Kostrzewski, D. H. Kim, G. Eichmann, “Optical position-coded multiple-valued logic and arithmetic using liquid-crystal TVs and holograms,” Opt. Commun. 70, 379–383 (1989).
[CrossRef]

Opt. Eng. (2)

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).

K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substitution,” Opt. Eng. 28, 364–372 (1989).

Opt. Lett. (3)

Other (3)

S. Kawai, Y. Kohga, “Modified signed-digit optical adder using computer-generated holograms,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 11B4.

S. Kawai, Y. Tashiro, I. Ogura, K. Yamada, K. Kasahara, “Optical crossbar interconnection with self-addressing,” in Conference Record of Topical Meeting on Optical Computing (Japan Society of Applied Physics, Tokyo, Japan, 1990), paper 10E7.

N. Nishida, Y. Ohta, Y. Ono, K. Kosuge, S. Sugama, M. Fujiwara, K. Kubota, S. Kawai, M. Sakaguchi, H. Kobayashi, H. Miyazaki, K. Shirakabe, “High-speed image sensor using holographic laser scanners,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper TUG2.

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Figures (16)

Fig. 1
Fig. 1

MSD addition principles.

Fig. 2
Fig. 2

MSD multiplication principles that use a handwritten technique.

Fig. 3
Fig. 3

Spatial coding for MSD numbers.

Fig. 4
Fig. 4

Proposed optical MSD adder: OBD, optical branching device; OTD, optical threshold device.

Fig. 5
Fig. 5

One-stage processor in an adder.

Fig. 6
Fig. 6

Transformation patterns.

Fig. 7
Fig. 7

Optical crossbar interconnection with a self-addressing function.

Fig. 8
Fig. 8

Proposed optical MSD multiplier.

Fig. 9
Fig. 9

Reconstructed CGH optics.

Fig. 10
Fig. 10

Amplitude adjustment effects.

Fig. 11
Fig. 11

CGH’s for bit-pattern transformation.

Fig. 12
Fig. 12

Sample CGH.

Fig. 13
Fig. 13

Diffracted light beam pattern of the CGH.

Fig. 14
Fig. 14

Current versus applied voltage characteristics for the VSTEP.

Fig. 15
Fig. 15

Two-bit diffraction pattern for transformation F1.

Fig. 16
Fig. 16

VSTEP array: (a) switched-off state; (b) one device switched on and omitting light.

Tables (3)

Tables Icon

Table I MSD Addition Rule

Tables Icon

Table II Conversion Rule from MSD to Binary

Tables Icon

Table III Specifications for the CGH

Equations (12)

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

A n - 1 A n - 2 A 0 + B n - 1 B n - 2 B 0 = C n C n - 1 C 0 ;
A n - 1 A n - 2 A 0 × B n - 1 B n - 2 B 0 = C 2 n - 1 C 2 n - 2 C 0 ;
I ( r ) = | j = 1 n A j exp ( i k r ) r j + A p exp ( i k r ) | 2 ,
r j ( ξ , η ) = [ ( x j - ξ ) 2 + ( y j - η ) 2 ] 1 / 2 ,
I ( ξ , η ) = Re ( ξ , η ) 2 + Im ( ξ , η ) 2 ,
Re ( ξ , η ) = j - 1 n cos [ r j ( ξ , η ) ] r j ( ξ , η ) + A p ,
Im ( ξ , η ) = j = 1 n sin [ r j ( ξ , η ) ] r j ( ξ , η ) .
A j A 0 = f sec θ 0 f sec θ j = cos θ j cos θ 0 ,
A j = cos θ 0 cos θ j A 0 .
ω = cos θ f 2 sec 2 θ = cos 3 θ f 2 .
I j I 0 = cos 3 θ j cos 3 θ 0 .
A j = cos 3 / 2 θ 0 cos 3 / 2 θ j ,

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