Optical implementation of an efficient modified signed-digit trinary addition

Optics and Laser Technology

Volumn 30, Issue 1, 1998, Pages 49-55

  Hossain, M M ^a   Ahmed, J U ^b   Awwal, A A S ^c   Michel, H E ^c  

^a Spectra Precision Software   (United States)

^b HEWLETT PACKARD COMPANY   (United States)

^c Wright State University   (United States)

Author keywords

Modified signed digit; Multivalued logic; Optical computing

Indexed keywords

DIGITAL ARITHMETIC; LOGIC CIRCUITS; MANY VALUED LOGICS; SIGNAL TO NOISE RATIO;

MODIFIED SIGNED DIGIT (MSD) NUMBERS; OPTICAL PROGRAMMABLE LOGIC ARRAYS;

OPTICAL DATA PROCESSING;

EID: 0031996055     PISSN: 00303992     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0030-3992(98)00015-2     Document Type: Article

References (36)

1. Avizienis A. Signed-digit number representation for fast parallel arithmetic. IRE Trans Electron Comput 1961;EC-10:389-400.
2. Karim MA, Awwal AAS. Optical computing: an introduction. New York: Wiley, 1992.
3. Proceedings of IEEE, Special Issue on Optical Computing Systems, November 1994; see also Appl Opt March 1994 Issue.
4. Dao TT, Campbell DM. Multiple valued logic: an implementation . Opt Eng 1986;25:14-21.
5. Hurst SL. Multiple valued logic: its status and its realization. Opt Eng 1986;25:44-55.
6. Johnson EL, Karim MA. Digital design: a pragmatic approach. Boston, MA: PWS-KENT, 1987.
7. Huang A. Parallel algorithm for optical digital computer. In: Proc. of IEEE 10th International Optical Computing Conference, 1983:13-17.
8. Bocker RP, Drake BL, Lasher ME, Henderson TB. Modified signed-digit addition and subtraction using optical symbolic substitution. Appl Opt 1986:2456-2457.
9. Brenner KH, Huang A, Streibl N. Digital optical computing with symbolic substitution. Appl Opt 1986;25:3054-60.
10. Cherri AK, Karim MA. Modified signed-digit arithmetic using an efficient symbolic substitution. Appl Opt 1988;27:3824-7.
11. Takagi N, Yasuura H, Yajima S. High speed VLSI multiplication algorithm with a redundant binary addition tree. IEEE Trans Comput 1985;C-34:789-95.
12. Li Y, Eichmann G. Conditional symbolic modified signed digit arithmetic using optical content-addressable memory logic elements. Appl Opt 1987;26:2328-33.
13. Li Y, Kim DH, Kostrzewski A, Eichmann G. Optical contentaddressable memory based single stage parallel modified signed digit arithmetic. Opt Lett 1989;14:1254-6.
14. Awwal AAS. Single step receded signed-digit binary arithmetic using optical symbolic substitution. Appl Opt 1992;31(17):3205-8.
15. Cherri AK. Symmetrically recoded modified single-digit optical addition and subtraction. Appl Opt 1995;33:4378-82.
16. Casasent D, Woodford P. Symbolic substitution modified signed-digit adder. Appl Opt 1994;33:1498-506.
17. Hwang K, Louri A. Optical multiplication and division using modified signed-digit symbolic substitution. Opt Eng 1989;28:364-72.
18. Li G, Liu L, Shao L, Yin Y, Hua J. Parallel optical negabinary arithmetic based on logic operations. Appl Opt 1997;36:1011-6.
19. Awwal AAS, Islam MN, Karim MA. Modified signed-digit trinary arithmetic using optical symbolic substitution. Appl Opt 1992;31:1687-94.
20. Alam MS, Karim MA, Awwal AAS, Westerkamp JJ. Optical processing based on higher-order trinary modified-signed-digit symbolic substitution. Appl Opt 1992;31:5614-21.
21. Mirsalehi MM, Gaylord TK. Logical minimization of multilevel coded function. Appl Opt 1986;25:3078-88.
22. Hossain MM, Ahmed JU, Awwal AAS. Efficient electronic implementation of modified signed-digit trinary carry free adder. In: Proceedings of IEEE-NAECON, 1993:185-189.
23. Arrathoon R, Kozaitis S. Architectural and performance considerations for a 107-instructions/sec opto-electronic central processing unit. Opt Lett 1987;12:956.
24. Ngo NQ, Binh LN. Fiber-optic array algebraic processing architectures. Appl Opt 1995;34:803-15.
25. Ha B, Li Y. Parallel modified signed-digit arithmetic using an opto-electronic shared content-addressable-memory processor. Appl Opt 1994;33:3647-62.
26. Li KJ, Jenkins BK. Optical parallel-access shared memory system: analysis and experimental demonstration. Appl Opt 1995;34:358-69.
27. Awwal AAS, Karim MA. Polarization-encoded optical shadow-casting: direct implementation of a carry free adder. Appl Opt 1989;28:785-90.
28. Zhou S, Campbell S, Wu W, Yeh P, Liu HK. Modified-signed-digit arithmetic for multi-input digital optical computing. Appl Opt 1994;33:1507-16.
29. Zhou S, Campbell S, Wu W, Yeh P, Liu HK. Two stage modified signed-digit optical computing by spatial data encoding and polarization multiplexing. Appl Opt 1995;34:793-802.
30. Sun DG, He LM, Wang NX, Weng ZH. Optoelectronic butterfly interconnection architecture of modified signed-digit arithmetic systems: fully parallel adder and subtracter. Appl Opt 1994;33:6755-61.
31. Kawai S, Kohga Y. Modified signed-digit processors using computer-generated holograms. Appl Opt 1992;31:6193-9.
32. Alam MS. Parallel optical computing using recoded trinary signed-digit numbers. Appl Opt 1994;33:4392-7.
33. Alam MS, Awwal AAS, Karim MA. Digital optical processing based on higher-order modified signed-digit symbolic substitution. Appl Opt 1992;31(14):2419-25.
34. Michel HE, Awwal AAS. Noise and crosstalk in an optical neural network. Proc. IEEE 1996 National Aerospace and Electronics Conference 1996;2:662-9.
35. Huang H, Itoh M, Yatagai T. Modified signed-digit arithmetic based on redundant bit representation. Appl Opt 1994;33:6146-56.
36. Parthasarathi R, Jhunjhunwala A. Symbolic substitution by means of one-of-many coding. Opt Eng 1995;34:1456-63.