Abstract

A compact two-step modified-signed-digit arithmetic-logic array processor is proposed. When the reference digits are programmed, both addition and subtraction can be performed by the same binary logic operations regardless of the sign of the input digits. The optical implementation and experimental demonstration with an electron-trapping device are shown. Each digit is encoded by a single pixel, and no polarization is included. Any combinational logic can be easily performed without optoelectronic and electro-optic conversions of the intermediate results. The system is compact, general purpose, simple to align, and has a high signal-to-noise ratio.

© 1999 Optical Society of America

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  1. D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
    [CrossRef]
  2. P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 23, 20–25 (1984).
    [CrossRef]
  3. D. Casasent, B. K. Taylor, “Banded-matrix high-performance algorithm and architecture,” Appl. Opt. 24, 1476–1480 (1985).
    [CrossRef] [PubMed]
  4. G. Li, L. Liu, L. Shao, Y. Yin, “Modified direct twos-complement parallel array multiplication algorithm for optical complex matrix operation,” Appl. Opt. 34, 1321–1328 (1995).
    [CrossRef] [PubMed]
  5. G. Li, L. Liu, L. Shao, Z. Wang, “Negabinary arithmetic algorithms for digital parallel optical computation,” Opt. Lett. 19, 1337–1339 (1994).
    [CrossRef] [PubMed]
  6. A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype position-encoded residue look-up table using laser diodes,” Opt. Commun. 61, 302–308 (1987).
    [CrossRef]
  7. 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).
    [CrossRef]
  8. K. Hwang, A. Louri, “Optical multiplication and division using modified-signed-digit symbolic substitution,” Opt. Eng. 28, 364–372 (1989).
    [CrossRef]
  9. B. Ha, Y. Li, “Parallel modified signed-digit arithmetic using an optoelectronic shared content-addressable-memory processor,” Appl. Opt. 33, 3647–3662 (1994).
    [CrossRef] [PubMed]
  10. D. Casasent, P. Woodford, “Symbolic substitution modified signed-digit optical adder,” Appl. Opt. 33, 1498–1506 (1994).
    [CrossRef] [PubMed]
  11. K. W. Wong, L. M. Cheng, “Optical modified signed-digit addition based on binary logical operations,” Opt. Laser Technol. 26, 213–217 (1994).
    [CrossRef]
  12. B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
    [CrossRef]
  13. 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]
  14. A. L. Cherri, M. A. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
    [CrossRef] [PubMed]
  15. S. Zhou, S. Campbell, P. Yeh, H.-K. Liu, “Two-stage modified signed-digit optical computing by spatial data encoding and polarization multiplexing,” Appl. Opt. 34, 793–802 (1995).
    [CrossRef] [PubMed]
  16. A. A. S. Awwal, “Recoded signed-digit binary addition-subtraction using optoelectronic symbolic substitution,” Appl. Opt. 31, 3205–3208 (1992).
    [CrossRef] [PubMed]
  17. M. S. Alam, A. A. S. Awwal, M. A. Karim, “Digital optical processing based on higher-order modified signed-digit symbolic substitution,” Appl. Opt. 31, 2419–2425 (1992).
    [CrossRef] [PubMed]
  18. M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3078–3088 (1986).
    [CrossRef] [PubMed]
  19. 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]
  20. H. Huang, M. Itoh, T. Yatagai, “Modified signed-digit arithmetic based on redundant bit representation,” Appl. Opt. 33, 6146–6156 (1994).
    [CrossRef] [PubMed]
  21. M. S. Alam, “Efficient trinary signed-digit symbolic arithmetic,” Opt. Lett. 19, 353–355 (1994).
    [CrossRef] [PubMed]
  22. M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, H. E. Michel, “Optical implementation of an efficient modified signed-digit binary addition,” Opt. Laser Technol. 30, 49–55 (1998).
    [CrossRef]
  23. M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
    [CrossRef]
  24. G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit arithmetic and its optical implementation,” Opt. Commun. 137, 389–396 (1997).
    [CrossRef]
  25. G. Li, L. Liu, L. Shao, Y. Yin, J. Hua, “Parallel optical negabinary arithmetic based on logic operations,” Appl. Opt. 36, 1011–1016 (1997).
    [CrossRef] [PubMed]
  26. S. Zhang, M. Karim, “One-step optical negabinary and modified signed-digit adder,” Opt. Laser Technol. 30, 193–198 (1998).
    [CrossRef]
  27. J. Tanida, Y. Ichioka, “Optical logic array processor using shadowgrams,” J. Opt. Soc. Am. 73, 800–809 (1983).
    [CrossRef]
  28. T. Yatagai, “Optical space-variant logic-gate array based on spatial encoding technique,” Opt. Lett. 11, 260–262 (1986).
    [CrossRef] [PubMed]
  29. Y. Li, G. Eichmann, R. R. Alfano, “Optical computing using hybrid encoded shadow-casting,” Appl. Opt. 25, 2636–2638 (1986).
    [CrossRef] [PubMed]
  30. M. Karim, A. A. S. Awwal, A. K. Cherri, “Polarization-encoded optical shadow-casting logic units: design,” Appl. Opt. 26, 2720–2725 (1987).
    [CrossRef] [PubMed]
  31. G. Li, L. Liu, J. Hua, “Unified optical negabinary arithmetic with polarization-encoded optical shadow-casting,” Opt. Laser Technol. 29, 221–227 (1997).
    [CrossRef]
  32. G. Eichmann, Y. Li, R. R. Alfano, “Optical binary coded ternary arithmetic and logic,” Appl. Opt. 25, 3113–3121 (1986).
    [CrossRef] [PubMed]
  33. F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).

1998

M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, H. E. Michel, “Optical implementation of an efficient modified signed-digit binary addition,” Opt. Laser Technol. 30, 49–55 (1998).
[CrossRef]

S. Zhang, M. Karim, “One-step optical negabinary and modified signed-digit adder,” Opt. Laser Technol. 30, 193–198 (1998).
[CrossRef]

1997

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit arithmetic and its optical implementation,” Opt. Commun. 137, 389–396 (1997).
[CrossRef]

G. Li, L. Liu, L. Shao, Y. Yin, J. Hua, “Parallel optical negabinary arithmetic based on logic operations,” Appl. Opt. 36, 1011–1016 (1997).
[CrossRef] [PubMed]

G. Li, L. Liu, J. Hua, “Unified optical negabinary arithmetic with polarization-encoded optical shadow-casting,” Opt. Laser Technol. 29, 221–227 (1997).
[CrossRef]

1996

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
[CrossRef]

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

1995

1994

1992

1989

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

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]

1988

1987

1986

1985

1984

P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 23, 20–25 (1984).
[CrossRef]

1983

Ahmed, J. U.

M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, H. E. Michel, “Optical implementation of an efficient modified signed-digit binary addition,” Opt. Laser Technol. 30, 49–55 (1998).
[CrossRef]

Ahuja, Y.

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
[CrossRef]

Alam, M. S.

Alfano, R. R.

Awwal, A. A. S.

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).
[CrossRef]

Campbell, S.

Carlotto, M.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
[CrossRef]

Casasent, D.

D. Casasent, P. Woodford, “Symbolic substitution modified signed-digit optical adder,” Appl. Opt. 33, 1498–1506 (1994).
[CrossRef] [PubMed]

D. Casasent, B. K. Taylor, “Banded-matrix high-performance algorithm and architecture,” Appl. Opt. 24, 1476–1480 (1985).
[CrossRef] [PubMed]

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
[CrossRef]

Chatterjea, A.

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
[CrossRef]

Cheng, H.

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit arithmetic and its optical implementation,” Opt. Commun. 137, 389–396 (1997).
[CrossRef]

Cheng, L. M.

K. W. Wong, L. M. Cheng, “Optical modified signed-digit addition based on binary logical operations,” Opt. Laser Technol. 26, 213–217 (1994).
[CrossRef]

Cherri, A. K.

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
[CrossRef]

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

Cherri, A. L.

Davies, D. K.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype position-encoded residue look-up table using laser diodes,” Opt. Commun. 61, 302–308 (1987).
[CrossRef]

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).
[CrossRef]

Eichmann, G.

Gaylord, T. K.

Goutzoulis, A. P.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype position-encoded residue look-up table using laser diodes,” Opt. Commun. 61, 302–308 (1987).
[CrossRef]

Gu, P.

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

Guilfoyle, P. S.

P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 23, 20–25 (1984).
[CrossRef]

Ha, B.

Hossain, M. M.

M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, H. E. Michel, “Optical implementation of an efficient modified signed-digit binary addition,” Opt. Laser Technol. 30, 49–55 (1998).
[CrossRef]

Hua, J.

G. Li, L. Liu, J. Hua, “Unified optical negabinary arithmetic with polarization-encoded optical shadow-casting,” Opt. Laser Technol. 29, 221–227 (1997).
[CrossRef]

G. Li, L. Liu, L. Shao, Y. Yin, J. Hua, “Parallel optical negabinary arithmetic based on logic operations,” Appl. Opt. 36, 1011–1016 (1997).
[CrossRef] [PubMed]

Huang, H.

Hwang, K.

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

Ichioka, Y.

Itoh, M.

Jing, H.

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit arithmetic and its optical implementation,” Opt. Commun. 137, 389–396 (1997).
[CrossRef]

Jutamulia, S.

F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).

Karim, M.

S. Zhang, M. Karim, “One-step optical negabinary and modified signed-digit adder,” Opt. Laser Technol. 30, 193–198 (1998).
[CrossRef]

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

Karim, M. A.

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).
[CrossRef]

Li, G.

Li, Y.

Liu, H.-K.

Liu, L.

Liu, X.

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

Louri, A.

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

Malarkey, E. C.

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype position-encoded residue look-up table using laser diodes,” Opt. Commun. 61, 302–308 (1987).
[CrossRef]

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).
[CrossRef]

Michel, H. E.

M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, H. E. Michel, “Optical implementation of an efficient modified signed-digit binary addition,” Opt. Laser Technol. 30, 49–55 (1998).
[CrossRef]

Mirsalehi, M. M.

Neft, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
[CrossRef]

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).
[CrossRef]

Psaltis, D.

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
[CrossRef]

Shao, L.

Tang, J.

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

Tanida, J.

Taylor, B. K.

Wang, B.

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

Wang, Z.

Wong, K. W.

K. W. Wong, L. M. Cheng, “Optical modified signed-digit addition based on binary logical operations,” Opt. Laser Technol. 26, 213–217 (1994).
[CrossRef]

Woodford, P.

Yatagai, T.

Yeh, P.

Yin, Y.

Yu, F.

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).

Zhang, S.

S. Zhang, M. Karim, “One-step optical negabinary and modified signed-digit adder,” Opt. Laser Technol. 30, 193–198 (1998).
[CrossRef]

Zhou, S.

Appl. Opt.

D. Casasent, B. K. Taylor, “Banded-matrix high-performance algorithm and architecture,” Appl. Opt. 24, 1476–1480 (1985).
[CrossRef] [PubMed]

G. Li, L. Liu, L. Shao, Y. Yin, “Modified direct twos-complement parallel array multiplication algorithm for optical complex matrix operation,” Appl. Opt. 34, 1321–1328 (1995).
[CrossRef] [PubMed]

B. Ha, Y. Li, “Parallel modified signed-digit arithmetic using an optoelectronic shared content-addressable-memory processor,” Appl. Opt. 33, 3647–3662 (1994).
[CrossRef] [PubMed]

D. Casasent, P. Woodford, “Symbolic substitution modified signed-digit optical adder,” Appl. Opt. 33, 1498–1506 (1994).
[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]

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

S. Zhou, S. Campbell, P. Yeh, H.-K. Liu, “Two-stage modified signed-digit optical computing by spatial data encoding and polarization multiplexing,” Appl. Opt. 34, 793–802 (1995).
[CrossRef] [PubMed]

A. A. S. Awwal, “Recoded signed-digit binary addition-subtraction using optoelectronic symbolic substitution,” Appl. Opt. 31, 3205–3208 (1992).
[CrossRef] [PubMed]

M. S. Alam, A. A. S. Awwal, M. A. Karim, “Digital optical processing based on higher-order modified signed-digit symbolic substitution,” Appl. Opt. 31, 2419–2425 (1992).
[CrossRef] [PubMed]

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

H. Huang, M. Itoh, T. Yatagai, “Modified signed-digit arithmetic based on redundant bit representation,” Appl. Opt. 33, 6146–6156 (1994).
[CrossRef] [PubMed]

G. Li, L. Liu, L. Shao, Y. Yin, J. Hua, “Parallel optical negabinary arithmetic based on logic operations,” Appl. Opt. 36, 1011–1016 (1997).
[CrossRef] [PubMed]

Y. Li, G. Eichmann, R. R. Alfano, “Optical computing using hybrid encoded shadow-casting,” Appl. Opt. 25, 2636–2638 (1986).
[CrossRef] [PubMed]

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

G. Eichmann, Y. Li, R. R. Alfano, “Optical binary coded ternary arithmetic and logic,” Appl. Opt. 25, 3113–3121 (1986).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

Opt. Commun.

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit arithmetic and its optical implementation,” Opt. Commun. 137, 389–396 (1997).
[CrossRef]

A. P. Goutzoulis, D. K. Davies, E. C. Malarkey, “Prototype position-encoded residue look-up table using laser diodes,” Opt. Commun. 61, 302–308 (1987).
[CrossRef]

Opt. Eng.

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).
[CrossRef]

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

P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 23, 20–25 (1984).
[CrossRef]

B. Wang, F. Yu, X. Liu, P. Gu, J. Tang, “Optical modified signed-digit addition module based on Boolean polarization-encoded logic algebra,” Opt. Eng. 35, 2989–2994 (1996).
[CrossRef]

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
[CrossRef]

Opt. Laser Technol.

S. Zhang, M. Karim, “One-step optical negabinary and modified signed-digit adder,” Opt. Laser Technol. 30, 193–198 (1998).
[CrossRef]

G. Li, L. Liu, J. Hua, “Unified optical negabinary arithmetic with polarization-encoded optical shadow-casting,” Opt. Laser Technol. 29, 221–227 (1997).
[CrossRef]

M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, H. E. Michel, “Optical implementation of an efficient modified signed-digit binary addition,” Opt. Laser Technol. 30, 49–55 (1998).
[CrossRef]

K. W. Wong, L. M. Cheng, “Optical modified signed-digit addition based on binary logical operations,” Opt. Laser Technol. 26, 213–217 (1994).
[CrossRef]

Opt. Lett.

Other

F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).

D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in 1980 International Optical Computing Conference II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Data-flow diagram for four-digit MSD addition and subtraction based on binary logic operations. T and W are binary functional units in the first step with the unsigned values of a i and b i and the binary reference bits g i and h i as the input. S is the binary functional unit in the second step with the unsigned values of t i and w i and the binary reference bit gi as the input.

Fig. 2
Fig. 2

Compact parallel MSD arithmetic-logic array processor with electron-trapping device.

Fig. 3
Fig. 3

Experimental results for the addition A1 + B1 and the subtraction A2 - B2 (numerical example in Section 2). (a), (b) The 1 and 1̅ outputs for T1 and T2; (c), (d) the 1 and 1̅ outputs for W1 and W2; (e), (f) the 1 and 1̅ outputs for the final sum S and the difference D.

Tables (4)

Tables Icon

Table 1 Modified Conditional Truth Table for the First Step of MSD Addition

Tables Icon

Table 2 Modified Conditional Truth Table for the First Step of MSD Subtraction

Tables Icon

Table 3 Truth Table for the Second Step of MSD Addition/Subtraction

Tables Icon

Table 4 Procedure for Performing the Binary Logic Operations Involved in the Two-Step MSD Addition/Subtractiona

Equations (8)

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

X=i=0N-1 xi2i,  xi  1¯, 0, 1.
output 1: aibigi+aibigigi-1,
output 1¯: hi+ai  big¯ig¯i-1.
output 1:ai  big¯i-1,
output 1¯:ai  bigi-1,
output 1:ti  wigi,
output 1¯:ti  wigi¯.
Addition: A1+B1Subtraction: A2-B2 A1: 1 0 1¯ 1¯ 1 1 1¯ 1¯ 8910 A2: 1¯ 0 1 1 1¯ 1¯ 1 0 -9010 B1: 1 1 1¯ 0 1 1 1¯ 0 17010 B2: 1 0 1¯ 0 1 1 1 1 11110Binary input: A1: 1 0 1 1 1 1 1 1 A2: 1 0 1 1 1 1 1 0 B1: 1 1 1 0 1 1 1 0 B2: 1 0 1 0 1 1 1 1 G1: 1 1 0 0 1 1 0 0 G2: 0 1 1 1 0 0 0 0 H1: 0 0 1 0 0 0 1 0  H2: 1 0 0 0 1 1 0 0 T1: 1 0 1¯ 0 1 0 1¯ 0 ϕ T2: 1¯ 0 1 0 1¯ 1¯ 0 0 ϕ W1: ϕ 0 1 0 1¯ 0 0 0 1¯ W2: ϕ 0 0 0 1 0 0 0 1¯ G1: 1 1 0 1 0 1 0 0 0 G2: 0 1 1 1 0 0 1 1 0 S: 1 0 0 0 0 1 1¯ 0 1¯ 25910 D: 1¯ 0 1 0 0 1¯ 001¯ -20110

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