Abstract

On the basis of the symmetric encoding algorithm for the modified signed-digit (MSD), a 7*7 truth table that can be realized with optical methods was developed. And based on the truth table, the optical path structures and circuit implementations of the one-step MSD adder of ternary optical computer (TOC) were designed. Experiments show that the scheme is correct, feasible, and efficient.

© 2012 Optical Society of America

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  1. H. John Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik 117, 199–209 (2006).
    [CrossRef]
  2. W. M. Wong and K. J. Blow, “Design and analysis of an all-optical processor for modular arithmetic,” Opt. Commun. 265, 425–433 (2006).
    [CrossRef]
  3. J. N. Roy and D. K. Gayen, “Integrated all-optical logic and arithmetic operations with the help of a TOAD-based interferometer device—alternative approach,” Appl. Opt. 46, 5304–5310 (2007).
    [CrossRef]
  4. N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Two-dimensional arrangement of spatial patterns representing numerical data in input images for effective use of hardware resources in digital optical computing system based on optical array logic,” J. Parallel Distr. Comput. 64, 1027–1040(2004).
    [CrossRef]
  5. N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Performance comparison and evaluation of options for arranging data in digital optical parallel computing,” Optical Review 10, 523–533 (2003).
    [CrossRef]
  6. Y. Jin, H. C. He, and Y. T. Lü, “Ternary optical computer principle,” Sci. China Ser. F 46, 145–150 (2003).
  7. Y. A. Zaghloul and A. R. M. Zaghloul, “Complete all-optical processing polarization-based binary logic gates and optical processors,” Opt. Express 14, 9879–9895 (2006).
    [CrossRef]
  8. Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7252–7269 (2006).
    [CrossRef]
  9. L. Teng, J. J. Peng, Y. Jin, and M. Li, “A cellular automata calculation model based on ternary optical computer,” in Proceedings of the 2nd International Conference on High Performance Computing and Applications (Springer, 2009), pp. 377–383.
  10. Z. Y. Shen, Y. Jin, and J. J. Peng, “Experimental system of ternary logic optical computer with reconfigurability,” Proc. SPIE 7282, 72823I (2009).
    [CrossRef]
  11. X. C. Wang, J. J. Peng, and S. Ouyang, “Control method for the optical components of a dynamically reconfigurable optical platform,” Appl. Opt. 50, 662–670 (2011).
    [CrossRef]
  12. M. M. Hossain, J. U. Ahmed, A. A. S. Awwal, and H. E. Michel, “Optical implementation of an efficient modified signed-digit trinary addition,” Opt. Laser Technol. 30, 49–55 (1998).
    [CrossRef]
  13. Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).
  14. A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. 10, 389–400 (1961).
    [CrossRef]
  15. B. L. Draker, R. P. Bocker, M. E. Lasher, R. H. Patterson, and W. J. Miceli, “Photonic computing using the modified signed-digit number representation,” Opt. Eng. 25, 38–43 (1986).
  16. M. Li, H. C. He, and Y. Jin, “A new method for optical vectormatrix multiplier,” in Proceedings of 2009 International Conference on Electronic Computer Technology (Computer Society, 2009), pp. 191–194.
  17. X. C. Wang, J. J. Peng, M. Li, Z. Y. Shen, and S. Ouyang, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010).
    [CrossRef]
  18. A. Cherri and M. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
    [CrossRef]
  19. A. A. S. Awwal, M. A. Karim, and A. K. Cherri, “Polarization-encoded optical shadow-casting scheme: design of multioutput trinary combinational logic units,” Appl. Opt. 26, 4814–4818 (1987).
    [CrossRef]
  20. A. Cherri, “Symmetrically recoded modified signed-digit optical addition and subtraction,” Appl. Opt. 33, 4378–4382 (1994).
    [CrossRef]
  21. A. Cherri and M. Alam, “Algorithms for optoelectronic implementation of modified signed-digit division, square-root, logarithmic, and exponential functions,” Appl. Opt. 40, 1236–1243 (2001).
    [CrossRef]
  22. S. Mukopadhyay, A. Basuray, and A. K. Das, “New coding scheme for addition and subtraction using the modified signed-digit number representation in optical computation,” Appl. Opt. 27, 1375–1376 (1988).
    [CrossRef]
  23. C. Taraphdar, T. Chattopadhyay, and J. N. Roy, “Designing of an all-optical scheme for single input ternary logical operations,” Optik Int. J. Light Electron Opt. 122, 33–36 (2011).
  24. A. A. S. Awwal, “Single step recoded signed-digit binary arithmetic using optical symbolic substitution,” Appl. Opt. 31, 3205–3208 (1992).
    [CrossRef]
  25. Y. Li, D. Kim, A. Kostrzewski, and G. Eichmann, “Content-addressable-memory-based single-stage optical modified-signed-digit arithmetic,” Opt. Lett. 14, 1254–1256 (1989).
    [CrossRef]
  26. J. Y. Yan, Y. Jin, and K. Z. Zuo, “Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer,” Sci. China Ser. F 51, 1415–1426 (2008).
  27. A. K. Maiti, J. N. Roy, and S. Mukopadhyay, “All-optical conversion scheme from binary to its MTN form with the help of nonlinear material based tree-net architecture,” Chin. Opt. Lett. 5, 480–483 (2007).
  28. T. Chattopadhyay, “All-optical symmetric ternary logic gate,” Opt. Laser Technol. 42, 1014–1021 (2010).
    [CrossRef]
  29. S. Mukopadhyay, “Binary optical data subtraction by using a ternary dibit representation technique in optical arithmetic problem,” Appl. Opt. 31, 4622–4623 (1992).
    [CrossRef]
  30. H. A. Kamal, “Parallel high radix negabinary signed digit arithmetic operations: one-step trinary and one-step quaternary addition algorithm,” Kuwait J. Sci. Eng. 31, 189–202 (2004).
  31. T. Chattopadhyay, G. K. Maity, and J. Nath Roy, “Designing of all optical tri-state logic system with the help of optical nonlinear material,” J. Nonlinear Opt. Phys. Mater. 17, 315–328 (2008).
    [CrossRef]
  32. T. Chattopadhyay, “All-optical quaternary circuits using quaternary Tgate,” Optik Int. J. Light Electron Opt. 121, 1784–1788 (2010).

2011

C. Taraphdar, T. Chattopadhyay, and J. N. Roy, “Designing of an all-optical scheme for single input ternary logical operations,” Optik Int. J. Light Electron Opt. 122, 33–36 (2011).

X. C. Wang, J. J. Peng, and S. Ouyang, “Control method for the optical components of a dynamically reconfigurable optical platform,” Appl. Opt. 50, 662–670 (2011).
[CrossRef]

2010

X. C. Wang, J. J. Peng, M. Li, Z. Y. Shen, and S. Ouyang, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010).
[CrossRef]

T. Chattopadhyay, “All-optical symmetric ternary logic gate,” Opt. Laser Technol. 42, 1014–1021 (2010).
[CrossRef]

T. Chattopadhyay, “All-optical quaternary circuits using quaternary Tgate,” Optik Int. J. Light Electron Opt. 121, 1784–1788 (2010).

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

2009

Z. Y. Shen, Y. Jin, and J. J. Peng, “Experimental system of ternary logic optical computer with reconfigurability,” Proc. SPIE 7282, 72823I (2009).
[CrossRef]

2008

T. Chattopadhyay, G. K. Maity, and J. Nath Roy, “Designing of all optical tri-state logic system with the help of optical nonlinear material,” J. Nonlinear Opt. Phys. Mater. 17, 315–328 (2008).
[CrossRef]

J. Y. Yan, Y. Jin, and K. Z. Zuo, “Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer,” Sci. China Ser. F 51, 1415–1426 (2008).

2007

2006

Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7252–7269 (2006).
[CrossRef]

Y. A. Zaghloul and A. R. M. Zaghloul, “Complete all-optical processing polarization-based binary logic gates and optical processors,” Opt. Express 14, 9879–9895 (2006).
[CrossRef]

H. John Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik 117, 199–209 (2006).
[CrossRef]

W. M. Wong and K. J. Blow, “Design and analysis of an all-optical processor for modular arithmetic,” Opt. Commun. 265, 425–433 (2006).
[CrossRef]

2004

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Two-dimensional arrangement of spatial patterns representing numerical data in input images for effective use of hardware resources in digital optical computing system based on optical array logic,” J. Parallel Distr. Comput. 64, 1027–1040(2004).
[CrossRef]

H. A. Kamal, “Parallel high radix negabinary signed digit arithmetic operations: one-step trinary and one-step quaternary addition algorithm,” Kuwait J. Sci. Eng. 31, 189–202 (2004).

2003

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Performance comparison and evaluation of options for arranging data in digital optical parallel computing,” Optical Review 10, 523–533 (2003).
[CrossRef]

Y. Jin, H. C. He, and Y. T. Lü, “Ternary optical computer principle,” Sci. China Ser. F 46, 145–150 (2003).

2001

1998

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

1994

1992

1989

1988

1987

1986

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

1961

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

Ahmed, J. U.

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

Alam, M.

Avizienis, A.

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

Awatsujib, Y.

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Two-dimensional arrangement of spatial patterns representing numerical data in input images for effective use of hardware resources in digital optical computing system based on optical array logic,” J. Parallel Distr. Comput. 64, 1027–1040(2004).
[CrossRef]

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Performance comparison and evaluation of options for arranging data in digital optical parallel computing,” Optical Review 10, 523–533 (2003).
[CrossRef]

Awwal, A. A. S.

Basuray, A.

Blow, K. J.

W. M. Wong and K. J. Blow, “Design and analysis of an all-optical processor for modular arithmetic,” Opt. Commun. 265, 425–433 (2006).
[CrossRef]

Bocker, R. P.

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

Chattopadhyay, T.

C. Taraphdar, T. Chattopadhyay, and J. N. Roy, “Designing of an all-optical scheme for single input ternary logical operations,” Optik Int. J. Light Electron Opt. 122, 33–36 (2011).

T. Chattopadhyay, “All-optical quaternary circuits using quaternary Tgate,” Optik Int. J. Light Electron Opt. 121, 1784–1788 (2010).

T. Chattopadhyay, “All-optical symmetric ternary logic gate,” Opt. Laser Technol. 42, 1014–1021 (2010).
[CrossRef]

T. Chattopadhyay, G. K. Maity, and J. Nath Roy, “Designing of all optical tri-state logic system with the help of optical nonlinear material,” J. Nonlinear Opt. Phys. Mater. 17, 315–328 (2008).
[CrossRef]

Cherri, A.

Cherri, A. K.

Das, A. K.

Ding, G. T.

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

Draker, B. L.

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

Eichmann, G.

Gayen, D. K.

He, H. C.

Y. Jin, H. C. He, and Y. T. Lü, “Ternary optical computer principle,” Sci. China Ser. F 46, 145–150 (2003).

M. Li, H. C. He, and Y. Jin, “A new method for optical vectormatrix multiplier,” in Proceedings of 2009 International Conference on Electronic Computer Technology (Computer Society, 2009), pp. 191–194.

Hossain, M. M.

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

Jin, Y.

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

Z. Y. Shen, Y. Jin, and J. J. Peng, “Experimental system of ternary logic optical computer with reconfigurability,” Proc. SPIE 7282, 72823I (2009).
[CrossRef]

J. Y. Yan, Y. Jin, and K. Z. Zuo, “Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer,” Sci. China Ser. F 51, 1415–1426 (2008).

Y. Jin, H. C. He, and Y. T. Lü, “Ternary optical computer principle,” Sci. China Ser. F 46, 145–150 (2003).

M. Li, H. C. He, and Y. Jin, “A new method for optical vectormatrix multiplier,” in Proceedings of 2009 International Conference on Electronic Computer Technology (Computer Society, 2009), pp. 191–194.

L. Teng, J. J. Peng, Y. Jin, and M. Li, “A cellular automata calculation model based on ternary optical computer,” in Proceedings of the 2nd International Conference on High Performance Computing and Applications (Springer, 2009), pp. 377–383.

John Caulfield, H.

H. John Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik 117, 199–209 (2006).
[CrossRef]

Kamal, H. A.

H. A. Kamal, “Parallel high radix negabinary signed digit arithmetic operations: one-step trinary and one-step quaternary addition algorithm,” Kuwait J. Sci. Eng. 31, 189–202 (2004).

Karim, M.

Karim, M. A.

Kim, D.

Kostrzewski, A.

Kubota, T.

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Two-dimensional arrangement of spatial patterns representing numerical data in input images for effective use of hardware resources in digital optical computing system based on optical array logic,” J. Parallel Distr. Comput. 64, 1027–1040(2004).
[CrossRef]

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Performance comparison and evaluation of options for arranging data in digital optical parallel computing,” Optical Review 10, 523–533 (2003).
[CrossRef]

Lasher, M. E.

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

Li, M.

X. C. Wang, J. J. Peng, M. Li, Z. Y. Shen, and S. Ouyang, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010).
[CrossRef]

M. Li, H. C. He, and Y. Jin, “A new method for optical vectormatrix multiplier,” in Proceedings of 2009 International Conference on Electronic Computer Technology (Computer Society, 2009), pp. 191–194.

L. Teng, J. J. Peng, Y. Jin, and M. Li, “A cellular automata calculation model based on ternary optical computer,” in Proceedings of the 2nd International Conference on High Performance Computing and Applications (Springer, 2009), pp. 377–383.

Li, Y.

Lü, Y. T.

Y. Jin, H. C. He, and Y. T. Lü, “Ternary optical computer principle,” Sci. China Ser. F 46, 145–150 (2003).

Maiti, A. K.

Maity, G. K.

T. Chattopadhyay, G. K. Maity, and J. Nath Roy, “Designing of all optical tri-state logic system with the help of optical nonlinear material,” J. Nonlinear Opt. Phys. Mater. 17, 315–328 (2008).
[CrossRef]

Miceli, W. J.

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

Michel, H. E.

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

Mukopadhyay, S.

Nath Roy, J.

T. Chattopadhyay, G. K. Maity, and J. Nath Roy, “Designing of all optical tri-state logic system with the help of optical nonlinear material,” J. Nonlinear Opt. Phys. Mater. 17, 315–328 (2008).
[CrossRef]

Nishimuraa, N.

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Two-dimensional arrangement of spatial patterns representing numerical data in input images for effective use of hardware resources in digital optical computing system based on optical array logic,” J. Parallel Distr. Comput. 64, 1027–1040(2004).
[CrossRef]

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Performance comparison and evaluation of options for arranging data in digital optical parallel computing,” Optical Review 10, 523–533 (2003).
[CrossRef]

Ouyang, S.

Patterson, R. H.

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

Peng, J. J.

X. C. Wang, J. J. Peng, and S. Ouyang, “Control method for the optical components of a dynamically reconfigurable optical platform,” Appl. Opt. 50, 662–670 (2011).
[CrossRef]

X. C. Wang, J. J. Peng, M. Li, Z. Y. Shen, and S. Ouyang, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010).
[CrossRef]

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

Z. Y. Shen, Y. Jin, and J. J. Peng, “Experimental system of ternary logic optical computer with reconfigurability,” Proc. SPIE 7282, 72823I (2009).
[CrossRef]

L. Teng, J. J. Peng, Y. Jin, and M. Li, “A cellular automata calculation model based on ternary optical computer,” in Proceedings of the 2nd International Conference on High Performance Computing and Applications (Springer, 2009), pp. 377–383.

Roy, J. N.

Shen, Y. F.

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

Shen, Z. Y.

X. C. Wang, J. J. Peng, M. Li, Z. Y. Shen, and S. Ouyang, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010).
[CrossRef]

Z. Y. Shen, Y. Jin, and J. J. Peng, “Experimental system of ternary logic optical computer with reconfigurability,” Proc. SPIE 7282, 72823I (2009).
[CrossRef]

Taraphdar, C.

C. Taraphdar, T. Chattopadhyay, and J. N. Roy, “Designing of an all-optical scheme for single input ternary logical operations,” Optik Int. J. Light Electron Opt. 122, 33–36 (2011).

Teng, L.

L. Teng, J. J. Peng, Y. Jin, and M. Li, “A cellular automata calculation model based on ternary optical computer,” in Proceedings of the 2nd International Conference on High Performance Computing and Applications (Springer, 2009), pp. 377–383.

Vikram, C. S.

H. John Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik 117, 199–209 (2006).
[CrossRef]

Wang, X. C.

Wong, W. M.

W. M. Wong and K. J. Blow, “Design and analysis of an all-optical processor for modular arithmetic,” Opt. Commun. 265, 425–433 (2006).
[CrossRef]

Yan, J. Y.

J. Y. Yan, Y. Jin, and K. Z. Zuo, “Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer,” Sci. China Ser. F 51, 1415–1426 (2008).

Yue, D. J.

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

Zaghloul, A. R. M.

Zaghloul, Y. A.

Zavalin, A.

H. John Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik 117, 199–209 (2006).
[CrossRef]

Zuo, K. Z.

J. Y. Yan, Y. Jin, and K. Z. Zuo, “Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer,” Sci. China Ser. F 51, 1415–1426 (2008).

Appl. Opt.

A. A. S. Awwal, M. A. Karim, and A. K. Cherri, “Polarization-encoded optical shadow-casting scheme: design of multioutput trinary combinational logic units,” Appl. Opt. 26, 4814–4818 (1987).
[CrossRef]

S. Mukopadhyay, A. Basuray, and A. K. Das, “New coding scheme for addition and subtraction using the modified signed-digit number representation in optical computation,” Appl. Opt. 27, 1375–1376 (1988).
[CrossRef]

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

S. Mukopadhyay, “Binary optical data subtraction by using a ternary dibit representation technique in optical arithmetic problem,” Appl. Opt. 31, 4622–4623 (1992).
[CrossRef]

A. Cherri, “Symmetrically recoded modified signed-digit optical addition and subtraction,” Appl. Opt. 33, 4378–4382 (1994).
[CrossRef]

A. Cherri and M. Alam, “Algorithms for optoelectronic implementation of modified signed-digit division, square-root, logarithmic, and exponential functions,” Appl. Opt. 40, 1236–1243 (2001).
[CrossRef]

J. N. Roy and D. K. Gayen, “Integrated all-optical logic and arithmetic operations with the help of a TOAD-based interferometer device—alternative approach,” Appl. Opt. 46, 5304–5310 (2007).
[CrossRef]

A. A. S. Awwal, “Single step recoded signed-digit binary arithmetic using optical symbolic substitution,” Appl. Opt. 31, 3205–3208 (1992).
[CrossRef]

X. C. Wang, J. J. Peng, M. Li, Z. Y. Shen, and S. Ouyang, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010).
[CrossRef]

X. C. Wang, J. J. Peng, and S. Ouyang, “Control method for the optical components of a dynamically reconfigurable optical platform,” Appl. Opt. 50, 662–670 (2011).
[CrossRef]

Chin. Opt. Lett.

IRE Trans. Electron. Comput.

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

J. Nonlinear Opt. Phys. Mater.

T. Chattopadhyay, G. K. Maity, and J. Nath Roy, “Designing of all optical tri-state logic system with the help of optical nonlinear material,” J. Nonlinear Opt. Phys. Mater. 17, 315–328 (2008).
[CrossRef]

J. Parallel Distr. Comput.

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Two-dimensional arrangement of spatial patterns representing numerical data in input images for effective use of hardware resources in digital optical computing system based on optical array logic,” J. Parallel Distr. Comput. 64, 1027–1040(2004).
[CrossRef]

Kuwait J. Sci. Eng.

H. A. Kamal, “Parallel high radix negabinary signed digit arithmetic operations: one-step trinary and one-step quaternary addition algorithm,” Kuwait J. Sci. Eng. 31, 189–202 (2004).

Opt. Commun.

W. M. Wong and K. J. Blow, “Design and analysis of an all-optical processor for modular arithmetic,” Opt. Commun. 265, 425–433 (2006).
[CrossRef]

Opt. Eng.

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

Opt. Express

Opt. Laser Technol.

T. Chattopadhyay, “All-optical symmetric ternary logic gate,” Opt. Laser Technol. 42, 1014–1021 (2010).
[CrossRef]

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

Opt. Lett.

Optical Review

N. Nishimuraa, Y. Awatsujib, and T. Kubota, “Performance comparison and evaluation of options for arranging data in digital optical parallel computing,” Optical Review 10, 523–533 (2003).
[CrossRef]

Optik

H. John Caulfield, C. S. Vikram, and A. Zavalin, “Optical logic redux,” Optik 117, 199–209 (2006).
[CrossRef]

Optik Int. J. Light Electron Opt.

T. Chattopadhyay, “All-optical quaternary circuits using quaternary Tgate,” Optik Int. J. Light Electron Opt. 121, 1784–1788 (2010).

C. Taraphdar, T. Chattopadhyay, and J. N. Roy, “Designing of an all-optical scheme for single input ternary logical operations,” Optik Int. J. Light Electron Opt. 122, 33–36 (2011).

Proc. SPIE

Z. Y. Shen, Y. Jin, and J. J. Peng, “Experimental system of ternary logic optical computer with reconfigurability,” Proc. SPIE 7282, 72823I (2009).
[CrossRef]

Sci. China Ser. F

Y. Jin, Y. F. Shen, J. J. Peng, G. T. Ding, and D. J. Yue, “Principles and construction of MSD adder in ternary optical computer,” Sci. China Ser. F 53, 2159–2168 (2010).

Y. Jin, H. C. He, and Y. T. Lü, “Ternary optical computer principle,” Sci. China Ser. F 46, 145–150 (2003).

J. Y. Yan, Y. Jin, and K. Z. Zuo, “Decrease-radix design principle for carrying/borrowing free multi-valued and application in ternary optical computer,” Sci. China Ser. F 51, 1415–1426 (2008).

Other

M. Li, H. C. He, and Y. Jin, “A new method for optical vectormatrix multiplier,” in Proceedings of 2009 International Conference on Electronic Computer Technology (Computer Society, 2009), pp. 191–194.

L. Teng, J. J. Peng, Y. Jin, and M. Li, “A cellular automata calculation model based on ternary optical computer,” in Proceedings of the 2nd International Conference on High Performance Computing and Applications (Springer, 2009), pp. 377–383.

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Figures (7)

Fig. 1.
Fig. 1.

The optical path structure of module 6.

Fig. 2.
Fig. 2.

The optical path structures of the other six modules.

Fig. 3.
Fig. 3.

TN-type stroke segment LCD (unit: mm).

Fig. 4.
Fig. 4.

Basic circuit structures.

Fig. 5.
Fig. 5.

Overall circuit structure of module 6.

Fig. 6.
Fig. 6.

Experimental screenshot of module 6.

Fig. 7.
Fig. 7.

Experimental results.

Tables (7)

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Table 1. Truth Table for T , W , T , and W Transformations

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Table 2. Symmetric Recoding Truth Table for MSD Numbers

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Table 3. The Truth Table of One-Step MSD Addition

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Table 4. The Truth Table of One-Step MSD Addition Represented by H , W , and V

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Table 5. The Truth Table of Module 6

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Table 6. The Truth Table of the Controller Optical Path

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Table 7. The Experimental Data

Equations (3)

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

X = i x i × 2 i .
( 7 ) 10 = ( 111 ) MSD = ( 100 ı ¯ ) MSD = ( 1 ı ¯ 00 ı ¯ ) MSD , ( 7 ) 10 = ( ı ¯ ı ¯ ı ¯ ) MSD = ( ı ¯ 001 ) MSD = ( ı ¯ 1001 ) MSD .
s = 111011 , w = ı ¯ 000 ı ¯ ı ¯ , t = 1110110 ; s = 0000000 w = 101010 ı ¯ , t = 00000000 .

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