OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 41, Iss. 8 — Mar. 10, 2002
  • pp: 1556–1564

Signed-negabinary-arithmetic-based optical computing by use of a single liquid-crystal-display panel

Asit K. Datta and Soumika Munshi  »View Author Affiliations

Applied Optics, Vol. 41, Issue 8, pp. 1556-1564 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (200 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique. For addition and subtraction, one of the operands in decimal form is converted into the unsigned negabinary form, whereas the other decimal number is represented in the signed negabinary form. The result of operation is obtained in the mixed negabinary form and is converted back into decimal. Matrix-vector multiplication for unsigned negabinary numbers is achieved through the convolution technique. Both of the operands for logical operation are converted to their signed negabinary forms. All operations are implemented by use of a unique optical architecture. The use of a single liquid-crystal-display panel to spatially encode the input data, operational kernels, and decoding masks have simplified the architecture as well as reduced the cost and complexity.

© 2002 Optical Society of America

OCIS Codes
(200.1130) Optics in computing : Algebraic optical processing
(200.4560) Optics in computing : Optical data processing
(200.4660) Optics in computing : Optical logic
(200.4860) Optics in computing : Optical vector-matrix systems

Original Manuscript: April 20, 2001
Revised Manuscript: November 26, 2001
Published: March 10, 2002

Asit K. Datta and Soumika Munshi, "Signed-negabinary-arithmetic-based optical computing by use of a single liquid-crystal-display panel," Appl. Opt. 41, 1556-1564 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Hwang, Computer Arithmetic: Principles, Architecture and Design (Wiley, New York, 1979).
  2. E. Swartzlander, “Digital optical arithmetic,” Appl. Opt. 25, 3021–3032 (1986). [CrossRef] [PubMed]
  3. A. Kostrzewski, D. H. Kim, Y. Li, G. Eichmann, “Fast hybrid parallel carry-ahead adder,” Opt. Lett. 15, 915–917 (1990). [CrossRef] [PubMed]
  4. A. K. Datta, M. Seth, “Parallel arithmetic operations in an optical architecture using a modified iterative technique,” Opt. Comm. 115, 245–250 (1995). [CrossRef]
  5. A. S. P. Kozaitis, “Higher-ordered rules for symbolic substitution,” Opt. Comm. 65, 339–342 (1988). [CrossRef]
  6. G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical higher-order symbolic recognition,” Appl. Opt. 29, 2135–2147 (1990). [CrossRef] [PubMed]
  7. 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]
  8. 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]
  9. Y. Wu, Z. Zhang, L. Liu, Z. Wang, “Arithmetic operation using binary encoding modified-signed-digit system,” Opt. Comm. 100, 53–58 (1993). [CrossRef]
  10. K. W. Wong, L. M. Cheng, “Optical modified signed-digit addition based on binary logical operations,” Opt. Laser Technol. 26, 213–217 (1994). [CrossRef]
  11. H. Huang, M. Itoh, T. Yatagai, “Modified signed-digit arithmetic based on redundant bit representation,” Appl. Opt. 33, 6146–6156 (1994). [CrossRef] [PubMed]
  12. 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]
  13. S. Zhang, M. A. Karim, “Programmable modified-signed-digit addition module based on binary logic gates,” Opt. Eng. 38, 456–461 (1999). [CrossRef]
  14. A. K. Datta, A. Basuray, S. Mukhopadhyay, “Arithmetic operations in optical computations using a modified trinary number system,” Opt. Lett. 14, 426–428 (1989). [CrossRef] [PubMed]
  15. M. S. Alam, M. A. Karim, A. A. S. Awwal, J. J. Westerkamp, “Optical processing based on conditional higher-order trinary modified signed-digit symbolic substitution,” Appl. Opt. 31, 5614–5621 (1992). [CrossRef] [PubMed]
  16. M. S. Alam, “Parallel optical computing using recoded trinary signed-digit numbers,” Appl. Opt. 33, 4392–4397 (1994). [CrossRef] [PubMed]
  17. M. S. Alam, K. Jemili, M. A. Karim, “Optical higher-order quaternary signed-digit arithmetic,” Opt. Eng. 33, 3419–3426 (1994). [CrossRef]
  18. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, “Optical computation using residue arithmetic,” Appl. Opt. 18, 149–162 (1979). [CrossRef] [PubMed]
  19. M. L. Heinrich, R. A. Athale, M. W. Huang, “Numerical optical computing in the residue number system with outer-product look-up tables,” Opt. Lett. 14, 847–849 (1989). [CrossRef] [PubMed]
  20. S. Mukhopadhyay, A. Basuray, A. K. Datta, “New technique of arithmetic operation using positional residue system,” App. Opt. 29, 2981–2893 (1990). [CrossRef]
  21. S. Zhang, M. A. Karim, “Optical arithmetic processing using improved redundant binary algorithms,” Opt. Eng. 38, 415–421 (1999). [CrossRef]
  22. A. K. Cherri, “Signed-digit arithmetic for optical computing: digit grouping and pixel assignment for spatial encoding,” Opt. Eng. 38, 422–431 (1999). [CrossRef]
  23. M. S. Alam, “Parallel optoelectronic trinary signed-digit division,” Opt. Eng. 38, 441–448 (1999). [CrossRef]
  24. C. Perlee, D. Casasent, “Negative base encoding in optical linear algebra processors,” Appl. Opt. 25, 168–169 (1986). [CrossRef] [PubMed]
  25. G. Li, L. Liu, L. Shao, Z. Wang, “Negative binary arithmetic algorithms for digital parallel optical computation,” Opt. Lett. 19, 1337–1339 (1994). [CrossRef] [PubMed]
  26. G. Li, L. Liu, Y. Yin, J. Hua, “Parallel optical negabinary arithmetic based on logic operations,” Appl. Opt. 36, 1011–1016 (1997). [CrossRef] [PubMed]
  27. G. Li, F. Qian, H. Ruan, L. Liu, “Parallel optical negabinary signed-digit computing: algorithm and optical implementation,” Opt. Eng. 38, 403–414 (1999). [CrossRef]
  28. J. Tanida, Y. Ichioka, “Optical logic array processor using shadowgrams,” J. Opt. Soc. Am. 73, 800–809 (1983). [CrossRef]
  29. J. Tanida, M. Iwata, Y. Ichioka, “Extended coding for optical array logic,” Appl. Opt. 33, 3363–3369 (1994). [CrossRef]
  30. A. K. Datta, M. Seth, “Multi-input optical parallel logic processing with the shadow-casting technique,” App. Opt. 33, 8146–8152 (1994). [CrossRef]
  31. D. Psaltis, D. Casasent, D. Neft, M. Carlotto, “Accurate numerical computation by optical convolution,” in Optical Computing II, W. T. Rhodes, ed., Proc. SPIE232, 151–156 (1980).
  32. S. Cartwright, “New optical matrix-vector multiplier,” Appl. Opt. 23, 1683–1684 (1984). [CrossRef] [PubMed]
  33. P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 23, 20–25 (1984). [CrossRef]
  34. S. Cartwright, S. C. Gustafson, “Convolver based optical systolic processing architecture,” Opt. Eng. 24, 59–62 (1985). [CrossRef]
  35. G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit multiplication and its use for matrix-vector operation,” Optik (Stuttgart) 107, 165–172 (1998).
  36. H. Huang, M. Itoh, T. Yatagai, “Optical scalable parallel modified signed-digit algorithms for large-scale array addition and multiplication using digit-decomposition-plane representation,” Opt. Eng. 38, 432–440 (1999). [CrossRef]
  37. S. Bandyopadhyay, A. K. Datta, S. S. Bawa, A. M. Biradar, S. Chandra, “Realization of digital optical matrix-vector multiplication,” J. Phys. D 28, 7–11 (1995). [CrossRef]
  38. G. Li, L. Liu, “Complex-valued matrix-vector multiplication using twos complement representation,” Opt. Comm. 105, 161–166 (1994). [CrossRef]
  39. G. Li, L. Liu, “Negabinary encoding for optical complex matrix operation,” Opt. Comm. 113, 15–19 (1994). [CrossRef]
  40. L. Liu, G. Li, Y. Yin, “Optical complex matrix-vector multiplication with negative binary inner products,” Opt. Lett. 19, 1759–1761 (1994). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited