## Optoelectronic Recoded and Nonrecoded Trinary Signed-Digit Adder that uses Optical Correlation

Applied Optics, Vol. 37, Issue 11, pp. 2153-2163 (1998)

http://dx.doi.org/10.1364/AO.37.002153

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### Abstract

A symbolic-substitution-based optical numeric processor that uses recoded and nonrecoded trinary signed-digit (TSD) number representations is proposed. Also, we propose new joint spatial encodings for the TSD numbers that reduce the symbolic-substitution computation rules involved in the processor. Optoelectronic implementation of the proposed recoded adder is feasible. Also, the nonrecoded TSD addition can be performed optically in two steps. Both the proposed recoded and nonrecoded adders are more compact than a recently reported modified signed-digit counterpart and use fewer correlators and spatial light modulators.

© 1998 Optical Society of America

**OCIS Codes**

(070.4550) Fourier optics and signal processing : Correlators

(200.0200) Optics in computing : Optics in computing

**Citation**

Abdallah K. Cherri, Mahmoud K. Habib, and Mohammad S. Alam, "Optoelectronic Recoded and Nonrecoded Trinary Signed-Digit Adder that uses Optical Correlation," Appl. Opt. **37**, 2153-2163 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-11-2153

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### References

- E. L. Johnson and M. A. Karim, Digital Design: A Pragmatic Approach (PWS-Kent, Boston, Mass., 1987).
- K. Hwang, Computer Arithmetic Principles: Architecture and Design (Wiley, New York, 1979).
- S. L. Hurst, “Multiple-valued threshold logic: its status and its realization,” Opt. Eng. 25, 44–53 (1986).
- M. M. Mirsalehi and T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3078–3088 (1986).
- A. P. Gautzouilis, E. C. Malarkey, D. K. Davies, J. C. Bradley, and P. R. Beaudet, “Optical processing with residue LED/LD lookup tables,” Appl. Opt. 27, 1674–1681 (1988).
- G. A. De Biase and A. Massini, “High efficiency redundant binary number representations for parallel arithmetic on optical computers,” Opt. Laser Technol. 26, 219–224 (1994).
- N. Takagi and S. Yajima, “Modular multiplication hardware algorithms with redundant representation and their application to RSA cryptosystem,” IEEE Trans. Comput. 41, 887–891 (1992).
- T. Stouraitis and C. Chen, “Hybrid signed-digit logarithmic number system processor,” Proc. Inst. Electr. Eng. Part E 140, 205–210 (1993).
- W. Balakrishnan and N. Burgess, “Very-high-speed VLSI 2s-complement multiplier using signed binary digits,” Proc. Inst. Electr. Eng. Part E 139, 29–34 (1992).
- F. Li and M. Morisue, “A novel Josephson adder without carry propagation delay,” IEEE Trans. Appl. Supercond. 3, 2683–2686 (1993).
- P. Srinivasan and F. E. Petry, “Constant-division algorithms,” Proc. Inst. Electr. Eng. Part E 141, 334–340 (1994).
- N. Burgess, “Radix-2 SRT division algorithm with simple quotient digit selection,” Electron. Lett. 27, 1910–1911 (1991).
- 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).
- A. K. Cherri and M. A. Karim, “Modified signed digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
- H. Huang, M. Itoh, and T. Yatagai, “Modified signed-digit arithmetic based on redundant bit representation,” Appl. Opt. 33, 6146–6156 (1994).
- A. A. S. Awwal, M. N. Islam, and M. A. Karim, “Modified signed-digit trinary arithmetic by using symbolic substitution,” Appl. Opt. 31, 1687–1694 (1994).
- A. K. Cherri, M. A. Habib, and M. S. Alam, “Efficient implementation of arithmetic units based on polarization-encoded optical shadow-casting,” Opt. Eng. 36, 94–101 (1997).
- 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, 5614–5622 (1992).
- A. K. Cherri, “Symmetrically recoded modified signed-digit optical addition and subtraction,” Appl. Opt. 33, 4378–4382 (1994).
- K. Hwang and D. K. Panda, “High-radix symbolic substitution and superposition techniques for optical matrix algebraic computations,” Opt. Eng. 31, 2422–2433 (1992).
- A. K. Cherri and N. I. Khachab, “Canonical quaternary signed-digit arithmetic using optoelectronics symbolic substitution,” Opt. Laser Technol. 28, 397–403 (1996).
- B. Ha and Y. Li, “Parallel modified signed-digit arithmetic using an optoelectronic shared content-addressable-memory processor,” Appl. Opt. 33, 3647–3662 (1994).
- M. S. Alam, Y. Ahuja, A. K. Cherri, and A. Chatterjea, “Symmetrically recoded quaternary signed-digit arithmetic using a shared content-addressable memory,” Opt. Eng. 35, 1141–1149 (1996).
- D. P. Casasent and E. C. Botha, “Multifunctional optical processor based on symbolic substitution,” Opt. Eng. 28, 425–433 (1989).
- E. Botha, J. Richards, and D. P. Casasent, “Optical laboratory morphological inspection processor,” Appl. Opt. 28, 5342–5350 (1989).
- D. P. Casasent and R. Sturgill, “Optical hit-or-miss morphological transforms for ATR,” in Applications of Digital Image Processing XII, J. Neffs, ed., Proc. SPIE 1153, 500–510 (1989).
- D. P. Casasent and E. C. Botha, “Optical correlator production system neural net,” Appl. Opt. 31, 1030–1040 (1992).
- K. Al-Ghoneim and D. P. Casasent, “High-accuracy pipelined iterative-tree optical multiplication,” Appl. Opt. 33, 1517–1527 (1994).
- M. S. Alam, “Parallel optical computing using recoded trinary signed-digit numbers,” Appl. Opt. 33, 4392–4397 (1994).
- D. P. Casasent and P. Woodford, “Symbolic substitution modified signed-digit optical adder,” Appl. Opt. 33, 1498–1506 (1994).
- A. Huang, “Parallel algorithms for optical digital computers,” in Proceedings of the Tenth International Optical Computing Conference, S. Horvitz, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1983), pp. 13–17.
- A. Louri, “Throughput enhancement for optical symbolic substitution systems,” Appl. Opt. 29, 2979–2980 (1990).
- A. Avizienis, “Signed-digit number representations for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
- H. E. Michel and A. A. S. Awwal, “Noise and cross talk study in an optical neural network,” in Proceedings of the National and Aerospace Electronics Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 662–669.
- R. P. Webb, “Performance of an optoelectronic neural network in the presence of noise,” Appl. Opt. 34, 5230–5240 (1995).
- S. Yamamoto, R. Sekura, J. Yamanaka, T. Ebihara, N. Kato, and H. Hosi, “Optical recognition with LAPS-SLM,” in Computer and Optically Formed Holographic Optics, I. Cindrich and S. H. Lee, eds., Proc. SPIE 1211, 273–283 (1990).
- M. Roe and K. Schnehrer, “High-speed and high-contrast operation of ferroelectric liquid crystal optically addressed spatial light modulators,” Opt. Eng. 32, 1662–1667 (1993).
- J. Gallant, “Futurebus+ standards spur commercial products,” Electron. Design News 37(18), 51–64 (1992).
- M. Jerome, “The fastest PCs in the world,” PC Computing 15 (8), 183–192 (1997).

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