Abstract

A high-accuracy fixed-point optical adder that operates in parallel on many long words and that uses a pipelined correlator architecture is described. A symbolic substitution algorithm with the modified signed-digit number representation is used to perform fixed-point additions with limited carries. A new set of substitution rules and encodings is developed to combine the recognition and substitution steps into one correlation operation. This reduces hardware requirements, improves throughput by reducing the space–bandwidth product needed, and reduces latency (the delay between when data enter the processor and when the final output is available) by a factor of 2. This algorithm and our new modified signed-digit encodings and substitution rules improve the performance of other correlator and noncorrelator optical numeric computing architectures.

© 1994 Optical Society of America

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References

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  1. E. Swartzlander, “The quasi-serial multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
    [CrossRef]
  2. H. Whitehouse, J. Speiser, “Linear signal processing architecture” in Aspects of Signal Processing—Part 2, G. Taconni, ed. (Reidel, Hingham, Mass., 1977), pp. 669–702.
  3. D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.232, 151–156 (1980).
  4. D. Psaltis, R. A. Athale, “High accuracy computation with linear analog optical systems: a critical study,” Appl. Opt. 25, 3071–3077 (1986).
    [CrossRef] [PubMed]
  5. A. P. Goutzoulis, “On the system efficiency of digital-accuracy acousto-optic processors,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 56–62 (1986).
  6. M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3078–3088 (1986).
    [CrossRef] [PubMed]
  7. Y. Li, D. 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]
  8. C. J. Perlee, D. P. Casasent, “Optical systems for digit-serial computation,” Appl. Opt. 28, 611–626 (1989).
    [CrossRef] [PubMed]
  9. V. P. Heuring, H. F. Jordan, J. P. Pratt, “Bit-serial architecture for optical computing,” Appl. Opt. 31, 3213–3224 (1992).
    [CrossRef] [PubMed]
  10. A. Huang, “Parallel algorithms for optical digital computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference, S. Horvitz, ed. (IEEE Computer Society Press, Silver Spring, Md., 1983), pp. 13–17.
  11. A. K. Cherri, M. A. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
    [CrossRef] [PubMed]
  12. 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]
  13. J. Tanida, Y. Ichoka, “Optical logic array processing using shadowgrams,” J. Opt. Soc. Am. 73, 800–809 (1983).
    [CrossRef]
  14. M. A. Karim, A. A. S. Awwal, A. K. Cherri, “Polarization-encoded optical shadow-casting logic units: design,” Appl. Opt. 26, 2720–2725 (1987).
    [CrossRef] [PubMed]
  15. A. K. Cherri, M. A. Karim, “Symbolic substitution based flagged arithmetic unit design using polarization-encoded optical shadow-casting system,” Opt. Commun. 70, 455–461 (1989).
    [CrossRef]
  16. J. Tanida, J. Nakagawa, Y. Ichioka, “Birefringent encoding and multichannel reflective correlator for optical array logic,” Appl. Opt. 27, 3819–3823 (1988).
    [CrossRef] [PubMed]
  17. K.-H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
    [CrossRef] [PubMed]
  18. K.-H. Brenner, “New implementation of symbolic substitution logic,” Appl. Opt. 25, 3061–3064 (1986).
    [CrossRef] [PubMed]
  19. P. A. Ramamoorthy, S. Antony, “Optical modified signed digit adder using polarization-coded symbolic substitution,” Opt. Eng. 26, 821–825 (1987).
  20. E. Botha, D. Casasent, E. Barnard, “Optical symbolic substitution using multichannel correlators,” Appl. Opt. 27, 817–818 (1988).
    [CrossRef] [PubMed]
  21. F. T. S. Yu, S. Jutamulia, “Implementation of symbolic substitution logic using optical associative memories,” Appl. Opt. 26, 2293–2294 (1987).
    [CrossRef] [PubMed]
  22. A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
    [CrossRef]
  23. D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on symbolic substitution,” Opt. Eng. 28, 425–433 (1989).
  24. K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substituion,” Opt. Eng. 28, 364–372 (1989).
  25. T. Parish, “Crystal clear storage,” Byte 15, 283–288 (1990).
  26. J. Gallant, “Futurebus+ standards spur commercial products,” Electron. Design News 37(18), 51–64 (1992).
  27. 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).
  28. N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).
  29. G. Moddel, P. R. Barbier, “Response time of a-Si:H photosensors in optically addressed spatial light modulators,” in Amorphous Silicon Technology—1991 Symposium, A. Madan, Y. Hamakawa, M. J. Thompson, P. C. Taylor, P. G. LeComber, eds. (Materials Research Society, Pittsburgh, Pa., 1991), pp. 155–165.
  30. H. S. Hinton, A. L. Lentine, “Multiple quantum-well technology takes SEED,” IEEE Circuits Devices 9, 12–18 (1993).
    [CrossRef]
  31. 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]
  32. S. Barua, “Carry-free optical binary adders,” in Optical Information-Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 573–579 (1990).
  33. 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]
  34. B. Telfer, D. P. Casasent, “Ho–Kashyap optical associative processors,” Appl. Opt. 29, 1191–1202 (1990).
    [CrossRef] [PubMed]
  35. A. Louri, “Throughput enhancement for optical symbolic substitution systems,” Appl. Opt. 29, 2979–2980 (1990).
    [CrossRef] [PubMed]
  36. K. Trivedi, M. Ercegovac, “On-line algorithms for division and multiplication,” IEEE Trans. Comput. C-26, 681–687 (1987).
    [CrossRef]

1993 (1)

H. S. Hinton, A. L. Lentine, “Multiple quantum-well technology takes SEED,” IEEE Circuits Devices 9, 12–18 (1993).
[CrossRef]

1992 (2)

J. Gallant, “Futurebus+ standards spur commercial products,” Electron. Design News 37(18), 51–64 (1992).

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Bit-serial architecture for optical computing,” Appl. Opt. 31, 3213–3224 (1992).
[CrossRef] [PubMed]

1990 (3)

1989 (5)

D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on symbolic substitution,” Opt. Eng. 28, 425–433 (1989).

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

Y. Li, D. 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]

C. J. Perlee, D. P. Casasent, “Optical systems for digit-serial computation,” Appl. Opt. 28, 611–626 (1989).
[CrossRef] [PubMed]

A. K. Cherri, M. A. Karim, “Symbolic substitution based flagged arithmetic unit design using polarization-encoded optical shadow-casting system,” Opt. Commun. 70, 455–461 (1989).
[CrossRef]

1988 (4)

1987 (5)

1986 (6)

1983 (1)

1973 (1)

E. Swartzlander, “The quasi-serial multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
[CrossRef]

1961 (1)

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

Antony, S.

P. A. Ramamoorthy, S. Antony, “Optical modified signed digit adder using polarization-coded symbolic substitution,” Opt. Eng. 26, 821–825 (1987).

Athale, R. A.

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.

Barbier, P. R.

G. Moddel, P. R. Barbier, “Response time of a-Si:H photosensors in optically addressed spatial light modulators,” in Amorphous Silicon Technology—1991 Symposium, A. Madan, Y. Hamakawa, M. J. Thompson, P. C. Taylor, P. G. LeComber, eds. (Materials Research Society, Pittsburgh, Pa., 1991), pp. 155–165.

Barnard, E.

Barua, S.

S. Barua, “Carry-free optical binary adders,” in Optical Information-Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 573–579 (1990).

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]

Botha, E.

Botha, E. C.

D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on symbolic substitution,” Opt. Eng. 28, 425–433 (1989).

Brenner, K.-H.

Carlotto, M.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.232, 151–156 (1980).

Casasent, D.

E. Botha, D. Casasent, E. Barnard, “Optical symbolic substitution using multichannel correlators,” Appl. Opt. 27, 817–818 (1988).
[CrossRef] [PubMed]

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.232, 151–156 (1980).

Casasent, D. P.

Cherri, A. K.

Datta, A. K.

Drake, B. L.

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]

Ebihara, T.

N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).

Eichmann, G.

Ercegovac, M.

K. Trivedi, M. Ercegovac, “On-line algorithms for division and multiplication,” IEEE Trans. Comput. C-26, 681–687 (1987).
[CrossRef]

Gallant, J.

J. Gallant, “Futurebus+ standards spur commercial products,” Electron. Design News 37(18), 51–64 (1992).

Gaylord, T. K.

Goutzoulis, A. P.

A. P. Goutzoulis, “On the system efficiency of digital-accuracy acousto-optic processors,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 56–62 (1986).

Henderson, T. B.

Heuring, V. P.

Hinton, H. S.

H. S. Hinton, A. L. Lentine, “Multiple quantum-well technology takes SEED,” IEEE Circuits Devices 9, 12–18 (1993).
[CrossRef]

Huang, A.

K.-H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
[CrossRef] [PubMed]

A. Huang, “Parallel algorithms for optical digital computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference, S. Horvitz, ed. (IEEE Computer Society Press, Silver Spring, Md., 1983), pp. 13–17.

Hwang, K.

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

Ichioka, Y.

Ichoka, Y.

Jordan, H. F.

Jutamulia, S.

Karim, M. A.

Kato, N.

N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).

Kim, D. H.

Kostrzewski, A.

Lasher, M. E.

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]

Lentine, A. L.

H. S. Hinton, A. L. Lentine, “Multiple quantum-well technology takes SEED,” IEEE Circuits Devices 9, 12–18 (1993).
[CrossRef]

Li, Y.

Louri, A.

A. Louri, “Throughput enhancement for optical symbolic substitution systems,” Appl. Opt. 29, 2979–2980 (1990).
[CrossRef] [PubMed]

K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substituion,” 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).

Mirsalehi, M. M.

Moddel, G.

G. Moddel, P. R. Barbier, “Response time of a-Si:H photosensors in optically addressed spatial light modulators,” in Amorphous Silicon Technology—1991 Symposium, A. Madan, Y. Hamakawa, M. J. Thompson, P. C. Taylor, P. G. LeComber, eds. (Materials Research Society, Pittsburgh, Pa., 1991), pp. 155–165.

Mukhopadhyay, S.

Nakagawa, J.

Neft, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.232, 151–156 (1980).

Parish, T.

T. Parish, “Crystal clear storage,” Byte 15, 283–288 (1990).

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).

Perlee, C. J.

Pratt, J. P.

Psaltis, D.

D. Psaltis, R. A. Athale, “High accuracy computation with linear analog optical systems: a critical study,” Appl. Opt. 25, 3071–3077 (1986).
[CrossRef] [PubMed]

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.232, 151–156 (1980).

Ramamoorthy, P. A.

P. A. Ramamoorthy, S. Antony, “Optical modified signed digit adder using polarization-coded symbolic substitution,” Opt. Eng. 26, 821–825 (1987).

Sekura, R.

N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).

Speiser, J.

H. Whitehouse, J. Speiser, “Linear signal processing architecture” in Aspects of Signal Processing—Part 2, G. Taconni, ed. (Reidel, Hingham, Mass., 1977), pp. 669–702.

Streibl, N.

Swartzlander, E.

E. Swartzlander, “The quasi-serial multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
[CrossRef]

Tanida, J.

Telfer, B.

Trivedi, K.

K. Trivedi, M. Ercegovac, “On-line algorithms for division and multiplication,” IEEE Trans. Comput. C-26, 681–687 (1987).
[CrossRef]

Whitehouse, H.

H. Whitehouse, J. Speiser, “Linear signal processing architecture” in Aspects of Signal Processing—Part 2, G. Taconni, ed. (Reidel, Hingham, Mass., 1977), pp. 669–702.

Yamamoto, S.

N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).

Yamanaka, J.

N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).

Yu, F. T. S.

Appl. Opt. (16)

D. Psaltis, R. A. Athale, “High accuracy computation with linear analog optical systems: a critical study,” Appl. Opt. 25, 3071–3077 (1986).
[CrossRef] [PubMed]

M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3078–3088 (1986).
[CrossRef] [PubMed]

C. J. Perlee, D. P. Casasent, “Optical systems for digit-serial computation,” Appl. Opt. 28, 611–626 (1989).
[CrossRef] [PubMed]

V. P. Heuring, H. F. Jordan, J. P. Pratt, “Bit-serial architecture for optical computing,” Appl. Opt. 31, 3213–3224 (1992).
[CrossRef] [PubMed]

A. K. Cherri, M. A. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
[CrossRef] [PubMed]

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]

M. A. Karim, A. A. S. Awwal, A. K. Cherri, “Polarization-encoded optical shadow-casting logic units: design,” Appl. Opt. 26, 2720–2725 (1987).
[CrossRef] [PubMed]

J. Tanida, J. Nakagawa, Y. Ichioka, “Birefringent encoding and multichannel reflective correlator for optical array logic,” Appl. Opt. 27, 3819–3823 (1988).
[CrossRef] [PubMed]

K.-H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
[CrossRef] [PubMed]

K.-H. Brenner, “New implementation of symbolic substitution logic,” Appl. Opt. 25, 3061–3064 (1986).
[CrossRef] [PubMed]

E. Botha, D. Casasent, E. Barnard, “Optical symbolic substitution using multichannel correlators,” Appl. Opt. 27, 817–818 (1988).
[CrossRef] [PubMed]

F. T. S. Yu, S. Jutamulia, “Implementation of symbolic substitution logic using optical associative memories,” Appl. Opt. 26, 2293–2294 (1987).
[CrossRef] [PubMed]

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. Telfer, D. P. Casasent, “Ho–Kashyap optical associative processors,” Appl. Opt. 29, 1191–1202 (1990).
[CrossRef] [PubMed]

A. Louri, “Throughput enhancement for optical symbolic substitution systems,” Appl. Opt. 29, 2979–2980 (1990).
[CrossRef] [PubMed]

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]

Byte (1)

T. Parish, “Crystal clear storage,” Byte 15, 283–288 (1990).

Electron. Design News (1)

J. Gallant, “Futurebus+ standards spur commercial products,” Electron. Design News 37(18), 51–64 (1992).

IEEE Circuits Devices (1)

H. S. Hinton, A. L. Lentine, “Multiple quantum-well technology takes SEED,” IEEE Circuits Devices 9, 12–18 (1993).
[CrossRef]

IEEE Trans. Comput. (2)

K. Trivedi, M. Ercegovac, “On-line algorithms for division and multiplication,” IEEE Trans. Comput. C-26, 681–687 (1987).
[CrossRef]

E. Swartzlander, “The quasi-serial multiplier,” IEEE Trans. Comput. C-22, 317–321 (1973).
[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]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. K. Cherri, M. A. Karim, “Symbolic substitution based flagged arithmetic unit design using polarization-encoded optical shadow-casting system,” Opt. Commun. 70, 455–461 (1989).
[CrossRef]

Opt. Eng. (4)

P. A. Ramamoorthy, S. Antony, “Optical modified signed digit adder using polarization-coded symbolic substitution,” Opt. Eng. 26, 821–825 (1987).

D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on symbolic substitution,” Opt. Eng. 28, 425–433 (1989).

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

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).

Opt. Lett. (1)

Other (7)

A. Huang, “Parallel algorithms for optical digital computers,” in Technical Digest, IEEE Tenth International Optical Computing Conference, S. Horvitz, ed. (IEEE Computer Society Press, Silver Spring, Md., 1983), pp. 13–17.

H. Whitehouse, J. Speiser, “Linear signal processing architecture” in Aspects of Signal Processing—Part 2, G. Taconni, ed. (Reidel, Hingham, Mass., 1977), pp. 669–702.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.232, 151–156 (1980).

A. P. Goutzoulis, “On the system efficiency of digital-accuracy acousto-optic processors,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 56–62 (1986).

N. Kato, R. Sekura, J. Yamanaka, T. Ebihara, S. Yamamoto, “Characteristics of a ferroelectric liquid crystal spatial light modulator with a dielectric mirror,” in Liquid-Crystal Devices and Materials, P. S. Drzaic, U. Efron, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1455, 190–205 (1991).

G. Moddel, P. R. Barbier, “Response time of a-Si:H photosensors in optically addressed spatial light modulators,” in Amorphous Silicon Technology—1991 Symposium, A. Madan, Y. Hamakawa, M. J. Thompson, P. C. Taylor, P. G. LeComber, eds. (Materials Research Society, Pittsburgh, Pa., 1991), pp. 155–165.

S. Barua, “Carry-free optical binary adders,” in Optical Information-Processing Systems and Architectures II, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1347, 573–579 (1990).

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Figures (7)

Fig. 1
Fig. 1

Basic SS cascaded correlator architecture.23 L’s, lenses.

Fig. 2
Fig. 2

Basic space- and frequency-multiplexed correlators.23 HOE, holographic optical element; L’s, lenses.

Fig. 3
Fig. 3

Block diagram of the optical memory–processor system.

Fig. 4
Fig. 4

Three-pixel MSD encoding27

Fig. 5
Fig. 5

Substitution rules33 for the first symbolic substitution stage of addition with the three-pixel MSD encoding of Fig. 4.

Fig. 6
Fig. 6

Flow chart of MSD-to-2’s complement algorithm that operates MSB to LSB.

Fig. 7
Fig. 7

Example of LSB-to-MSB MSD-to-2’s complement conversion.

Equations (19)

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

[ ( 200 pixels / mm ) ( 25 mm ) ] 2 100 μ s = 2.5 × 10 11 pixels / s .
X = [ o o o z z z b b b o z b o z b o z b ] ,
Y 1 = [ o o z o z b z b b z b z b z o z o z ] ,
A 1 = Y 1 X + = Y 1 X ( X T X ) - 1 ,
Y 1 = A 1 X = [ o o z o z b z b b z b z b z o z o z ] = [ A 11 A 12 A 21 A 22 ] [ o o o z z z b b b o z b o z b o z b ] .
z = A 21 z + A 22 z = ( A 21 + A 22 ) z
z = A 21 o + A 22 o = ( A 21 + A 22 ) o
X = [ o + o o + z o + b z + z z + b b + b ] ,
Y 1 = [ o o z z b b z b z z o z ]
1 o = [ 1 0 0 1 1 0 ] T , 0 z = [ 0 1 0 1 0 1 ] T , 1 ¯ b = [ 0 0 1 0 1 1 ] T .
X = [ 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 ] , Y 1 = [ 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 ] .
A 1 = [ 0 0 - 1 0 1 0 0 - 1 0 1 - 1 1 - 1 0 0 0 1 0 0 - 1 - 1 1 0 1 - 1 0 - 1 0 2 0 - 1 - 1 0 1 0 1 0 1 1 0 0 - 1 - 2 - 3 - 2 2 1 2 1 1 0 - 1 0 0 - 2 - 2 - 1 2 1 1 1 2 1 - 1 0 - 1 - 1 - 2 - 2 1 1 2 ] .
Y 2 = [ 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 ] , A 2 = [ - 1 - 1 - 1 1 1 0 1 1 1 0 - 1 0 - 1 - 1 - 1 0 1 1 0 0 0 1 0 0 - 2 - 2 - 2 1 2 1 0 0 0 0 0 1 1 1 0 - 1 0 0 - 2 - 3 - 2 2 1 2 0 1 1 0 0 - 1 - 1 - 2 - 2 1 1 2 1 2 1 - 1 0 - 1 - 2 - 2 - 1 2 1 1 ] .
1 o = [ 1 1 0 0 ] T , 0 z = [ 0 0 1 1 ] T , 1 ¯ b = [ 1 0 1 0 ] T .
X = [ 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 ] .
Y 1 = [ 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 ] , Y 2 = [ 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 ] .
A 1 = [ 0.36 0.55 0.36 - 0.45 0.09 0.64 0.09 - 0.36 0.36 - 0.45 0.36 0.55 0.09 - 0.36 0.09 0.64 0.82 - 0.27 - 0.18 0.73 0.64 - 0.55 - 0.36 0.45 - 0.18 0.73 0.82 - 0.27 - 0.36 0.45 0.64 - 0.55 ] , A 2 = [ 1.00 0.00 0.00 0.00 0.45 0.18 - 0.55 0.18 0.00 0.00 1.00 0.00 - 0.55 0.18 0.45 0.18 - 0.18 0.73 0.82 - 0.27 - 0.36 0.45 0.64 - 0.55 0.82 - 0.27 - 0.18 0.73 0.64 - 0.55 - 0.36 0.45 ] .
A 1 X = [ 0.91 1.27 0.82 0.73 0.27 - 0.09 0.73 0.82 0.45 0.18 - 0.18 - 0.27 - 0.09 0.27 0.82 0.73 1.27 0.91 - 0.27 - 0.18 0.45 0.18 0.82 0.73 0.55 0.36 1.09 0.64 1.36 0.55 0.09 - 0.27 0.18 0.27 0.73 0.09 0.55 1.36 1.09 0.64 0.36 0.55 0.09 0.73 0.18 0.27 - 0.27 0.09 ] , A 2 X = [ 1.00 1.00 1.00 1.00 1.00 0.00 0.64 0.09 0.27 - 0.09 0.09 - 0.36 0.00 1.00 1.00 1.00 1.00 1.00 - 0.36 0.09 0.27 - 0.09 0.09 0.64 0.55 1.36 1.09 0.64 0.36 0.55 0.09 0.73 0.18 0.27 - 0.27 0.09 0.55 0.36 1.09 0.64 1.36 0.55 0.09 - 0.27 0.18 0.27 0.73 0.09 ] .
thresh ( A 1 X ) = [ 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 ] , thresh ( A 2 X ) = [ 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 ] .

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