Abstract

Two opto-electronic implementations of carry-free addition and borrow-free subtraction of recoded signed-digit binary numbers that use optical symbolic substitution are proposed.

© 1992 Optical Society of America

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References

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  1. A. Avizienis, “Signed-digit number representation for fast parallel arithmetic,” IRE Trans. Electron. Comput. EC-10, 389–400 (1961).
    [CrossRef]
  2. A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991).
  3. A. Huang, “Parallel algorithm for optical digital computer,” in Proceedings of the IEEE 10th International Optical Computing Conference (Institute of Electrical and Electronics Engineers, New York, 1983), p. 13.
    [CrossRef]
  4. K. H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
    [CrossRef] [PubMed]
  5. 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]
  6. A. K. Cherri, M. A. Karim, “Modified signed-digit arithmetic using an efficient symbolic substitution,” Appl. Opt. 27, 3824–3827 (1988).
    [CrossRef] [PubMed]
  7. 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]
  8. M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3038–3088 (1986).
    [CrossRef]
  9. B. Parhami, “Carry-free addition of recoded binary signed-digit numbers,” IEEE Trans. Comput. 37, 1470–1476 (1988).
    [CrossRef]
  10. E. L. Johnson, M. A. Karim, Digital Design: a Pragmatic Approach (PWS-Kent, Boston, Mass., 1987).
  11. M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992).
  12. Y. Li, D. H. Kim, A. Kostrzewski, G. Eichmann, “Content-addressable-memory-based single-stage optical modified-signed-digit arithmetic,” Opt. Lett. 14, 1254–1256 (1989).
    [CrossRef] [PubMed]
  13. S. Barua, “Single-stage optical adder/subtracter,” Opt. Eng. 30, 265–270 (1991).
    [CrossRef]
  14. M. M. Mirsalehi, T. K. Gaylord, “Truth-table lookup optical parallel processing using content addressable memory,” Appl. Opt. 25, 2277–2283 (1986).
    [CrossRef] [PubMed]
  15. E. Botha, D. P. Casasent, E. Barnard, “Optical symbolic substitution using multichannel correlators,” Appl. Opt. 27, 817–818 (1988).
    [CrossRef] [PubMed]
  16. M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
    [CrossRef] [PubMed]
  17. A. A. S. Awwal, M. A. Karim, “Polarization-encoded optical shadow-casting: design of a carry-free adder,” Appl. Opt. 28, 785–790 (1989).
    [CrossRef] [PubMed]
  18. A. A. S. Awwal, A. D. McAulay, J. Wang, “Demonstration of a full adder using liquid crystal light valve and spatial light rebroadcaster,” in Annual Meeting Technical Digest, Vol. 17 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 73.

1991

S. Barua, “Single-stage optical adder/subtracter,” Opt. Eng. 30, 265–270 (1991).
[CrossRef]

1990

1989

1988

1987

1986

1961

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

Avizienis, A.

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

Awwal, A. A. S.

A. A. S. Awwal, M. A. Karim, “Polarization-encoded optical shadow-casting: design of a carry-free adder,” Appl. Opt. 28, 785–790 (1989).
[CrossRef] [PubMed]

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992).

A. A. S. Awwal, A. D. McAulay, J. Wang, “Demonstration of a full adder using liquid crystal light valve and spatial light rebroadcaster,” in Annual Meeting Technical Digest, Vol. 17 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 73.

Barnard, E.

Barua, S.

S. Barua, “Single-stage optical adder/subtracter,” Opt. Eng. 30, 265–270 (1991).
[CrossRef]

Bocker, R. P.

Botha, E.

Brenner, K. H.

Casasent, D. P.

Cherri, A. K.

Drake, B. L.

Eichmann, G.

Gaylord, T. K.

M. M. Mirsalehi, T. K. Gaylord, “Truth-table lookup optical parallel processing using content addressable memory,” Appl. Opt. 25, 2277–2283 (1986).
[CrossRef] [PubMed]

M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3038–3088 (1986).
[CrossRef]

Guest, C. C.

Henderson, T. B.

Huang, A.

K. H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
[CrossRef] [PubMed]

A. Huang, “Parallel algorithm for optical digital computer,” in Proceedings of the IEEE 10th International Optical Computing Conference (Institute of Electrical and Electronics Engineers, New York, 1983), p. 13.
[CrossRef]

Johnson, E. L.

E. L. Johnson, M. A. Karim, Digital Design: a Pragmatic Approach (PWS-Kent, Boston, Mass., 1987).

Karim, M. A.

Kim, D. H.

Kim, M. S.

Kostrzewski, A.

Lasher, M. E.

Li, Y.

McAulay, A. D.

A. A. S. Awwal, A. D. McAulay, J. Wang, “Demonstration of a full adder using liquid crystal light valve and spatial light rebroadcaster,” in Annual Meeting Technical Digest, Vol. 17 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 73.

A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991).

Mirsalehi, M. M.

M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3038–3088 (1986).
[CrossRef]

M. M. Mirsalehi, T. K. Gaylord, “Truth-table lookup optical parallel processing using content addressable memory,” Appl. Opt. 25, 2277–2283 (1986).
[CrossRef] [PubMed]

Parhami, B.

B. Parhami, “Carry-free addition of recoded binary signed-digit numbers,” IEEE Trans. Comput. 37, 1470–1476 (1988).
[CrossRef]

Streibl, N.

Wang, J.

A. A. S. Awwal, A. D. McAulay, J. Wang, “Demonstration of a full adder using liquid crystal light valve and spatial light rebroadcaster,” in Annual Meeting Technical Digest, Vol. 17 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 73.

Appl. Opt.

M. M. Mirsalehi, T. K. Gaylord, “Logical minimization of multilevel coded functions,” Appl. Opt. 25, 3038–3088 (1986).
[CrossRef]

M. M. Mirsalehi, T. K. Gaylord, “Truth-table lookup optical parallel processing using content addressable memory,” Appl. Opt. 25, 2277–2283 (1986).
[CrossRef] [PubMed]

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]

K. H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution,” Appl. Opt. 25, 3054–3060 (1986).
[CrossRef] [PubMed]

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]

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

A. A. S. Awwal, M. A. Karim, “Polarization-encoded optical shadow-casting: design of a carry-free adder,” Appl. Opt. 28, 785–790 (1989).
[CrossRef] [PubMed]

M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
[CrossRef] [PubMed]

E. Botha, D. P. Casasent, E. Barnard, “Optical symbolic substitution using multichannel correlators,” Appl. Opt. 27, 817–818 (1988).
[CrossRef] [PubMed]

IEEE Trans. Comput.

B. Parhami, “Carry-free addition of recoded binary signed-digit numbers,” IEEE Trans. Comput. 37, 1470–1476 (1988).
[CrossRef]

IRE Trans. Electron. Comput.

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

Opt. Eng.

S. Barua, “Single-stage optical adder/subtracter,” Opt. Eng. 30, 265–270 (1991).
[CrossRef]

Opt. Lett.

Other

A. A. S. Awwal, A. D. McAulay, J. Wang, “Demonstration of a full adder using liquid crystal light valve and spatial light rebroadcaster,” in Annual Meeting Technical Digest, Vol. 17 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 73.

A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991).

A. Huang, “Parallel algorithm for optical digital computer,” in Proceedings of the IEEE 10th International Optical Computing Conference (Institute of Electrical and Electronics Engineers, New York, 1983), p. 13.
[CrossRef]

E. L. Johnson, M. A. Karim, Digital Design: a Pragmatic Approach (PWS-Kent, Boston, Mass., 1987).

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992).

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Figures (4)

Fig. 1
Fig. 1

(a) Coding for MSD numbers; (b) CAM implementation.

Fig. 2
Fig. 2

(a) Triple-rail input encoding. Nonholographic CAM for generating (b) 1 and (c) 1 ¯ outputs in the recoding stage.

Fig. 3
Fig. 3

CAM for generating the final sum of 1 and 1 ¯.

Tables (2)

Tables Icon

Table I Recoding Truth Table for MSD Carry-Free Additiona

Tables Icon

Table II Addition Truth Table for RMSD Numbers

Metrics