Parallel optoelectronic trinary signed-digit division

Optical Engineering

Volumn 38, Issue 1-3, 1999, Pages 441-447

  Alam, Mohammad S ^a  

^a PURDUE UNIVERSITY FORT WAYNE   (United States)

Author keywords

Content addressable memory; Division algorithm; Optical computing; Symbolic substitution; Trinary signed digit

Indexed keywords

EID: 0001273950     PISSN: 00913286     EISSN: None     Source Type: Journal    
DOI: 10.1117/1.602120     Document Type: Article

References (36)

1. T. K. Gaylord, M. M. Mirsalehi, and C. C. Guest, "Optical digital truth-table look-up processing, " Opt. Eng. 24, 48-58 (1985).
2. A. Louri, "Parallel implementation of optical symbolic substitution logic using shadow-casting and polarization, " Appl. Opt. 30, 540-548 (1991).
3. M. M. Mirsalehi and T. K. Gaylord, "Truth-table look-up parallel processing using an optical content-addressable memory, " Appl. Opt. 25, 2277-2283 (1986).
4. N. Takagi, H. Yasura, and S. Yajima, "High speed VLSI multiplication algorithm with a redundant binary addition tree, " IEEE Trans. Comput. C-34, 789-795 (1985).
5. M. S. Alam, M. A. Karim, A. A. S. Awwal, and J. J. Westerkamp, "Optical processing based on conditional higher-order trinary modified signed-digit symbolic substitution, " Appl. Opt. 31, 5614-5621 (1992).
6. A. Avizienis, "Signed-digit number representation for fast parallel arithmetic, " IRE Trans. Electron. Comput. EC-10, 389-400 (1961).
7. K. Hwang and D. K. Panda, "High-radix symbolic substitution and superposition techniques for optical matrix algebraic computations, " Opt. Eng. 31, 2422-2433 (1992).
8. B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, and W. J. Miceli, "Photonic computing using modified signed-digit number representation, " Opt. Eng. 25, 38-43 (1986).
9. 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).
10. R. Arrathoon and S. P. Kozaitis, "Shadow casting for multiple-valued associated logic, " Opt. Eng. 25, 29-37 (1986).
11. K. H. Brenner, A. Huang, and N. Streibl, "Digital optical computing with symbolic substitution, " Appl. Opt. 25, 3054-3060 (1986).
12. R. P. Bocker, B. L. Drake, M. E. Lasher, and T. B. Henderson, "Modified signed-digit addition and subtraction using optical symbolic substitution, " Appl. Opt. 25, 2456-2457 (1986).
13. A. K. Cherri and M. A. Karim, "Modified signed-digit arithmetic using an efficient symbolic substitution, " Appl. Opt. 27, 3824-3827 (1988).
14. Y. Li and G. Eichmann, "Conditional symbolic modified signed-digit arithmetic using optical content-addressable memory logic elements, " Appl. Opt. 26, 2328-2333 (1987).
15. Y. Li, D. H. Kim, A. Kostrzewski, and G. Eichmann, "Content-addressable-memory-based single-stage optical modified signed-digit arithmetic, " Opt. Lett. 14, 1254-1256 (1989).
16. S. Barua, "High-speed multiplier for digital signal processing, " Opt. Eng. 30, 1997-2002 (1991).
17. A. Huang, "Parallel algorithms for optical digital computers, " in Proc. 10th Int. Optical Computing Conf., IEEE Computer Society, pp. 13-17, Los Angeles (1983).
18. K. H. Brenner, A. W. Lohmann, and T. K. Merklein, "Symbolic substitution implemented by spatial filtering logic, " Opt. Eng. 28, 390-395 (1989).
19. E. Botha, D. Casasent, and E. Barnhard, "Optical symbolic substitution using multichannel correlators, " Appl. Opt. 27, 817-818 (1987).
20. J. N. Mait and K. H. Brenner, "Optical symbolic substitution: system design using phase-only holograms, " Appl. Opt. 27, 1692-1700 (1988).
21. R. Thalmann, G. Pedrini, and K. J. Weible, "Optical symbolic substitution using diffraction gratings, " Appl. Opt. Commun. 29, 2126-2134 (1990).
22. S. Zhou, S. Campbell, P. Yeh, and H. K. Liu, "Modified signed-digit optical computing using fan-out elements, " Opt. Lett. 17, 1697-1699 (1992).
23. B. Parhami, "Carry-free addition of binary signed-digit numbers, " IEEE Trans. Comput. 37, 1470-1476 (1988).
24. A. A. S. Awwal, "Recoded signed-digit binary addition-subtraction using optoelectronic symbolic substitution, " Appl. Opt. 31, 3205-3208 (1992).
25. M. S. Alam, "Parallel optical computing using recoded trinary signed-digit numbers, " Appl. Opt. 33, 4392-4397 (1994).
26. Berlin Ha and Y. Li, "Parallel modified signed-digit arithmetic using an optoelectronic shared content-addressable-memory processor, " Appl. Opt. 33, 3647-3662 (1994).
27. M. S. Alam, Y. Ahuja, A. K. Cherri, and A. Chatterjea, "Symmetrically recoded quaternary signed-digit arithmetic using shared content-addressable memory, " Opt. Eng. 35, 1141-1149 (1996).
28. A. K. Cherri, M. K. Habib, and M. S. Alam, "Optoelectronic recoded and non-recoded trinary signed-digit adder that uses optical correlation, " Appl. Opt. 37, 2153-2163 (1998).
29. D. P. Casasent and P. Woodford, "Symbolic substitution modified signed-digit optical adder, " Appl. Opt. 33, 1498-1506 (1994).
30. A. K. Cherri and M. S. Alam, "Recoded and non-recoded trinary signed-digit adders and multipliers using redundant bit representation, " Appl. Opt. (in press).
31. A. Louri, "Throughput enhancement for optical symbolic substitution systems, " Appl. Opt. 29, 2979-2980 (1990).
32. K. Hwang and A. Louri, "Optical multiplication and division using modified signed-digit symbolic substitution, " Opt. Eng. 28, 364-372 (1989).
33. K. Al-Ghoneim and D. P. Casasent, "High accuracy pipelined iterative-tree optical multiplication, " Appl. Opt. 33, 1517-1527 (1994).
34. A. R. Omondi, Computer Arithmetic Systems, Prentice-Hall, Englewood Cliffs, NJ (1994).
35. K. Hwang and A. Louri, "Optical arithmetic using symbolic signed-digit substitution, " in Proc. 17th Int. Conf. on Parallel Processing, pp. 55-64, Pennsylvania State University Press (1988).
36. E. V. Krishnamurthy, "On optimal iterative schemes for high speed division, " IEEE Trans. Comput. C-19, 227-231 (1970).