Parallel Arithmetic on Optical Computers by Redundant Binary Number Representations

  • Giuseppe A. De Biase
  • Annalisa Massini


A parallel arithmetic, suitable for optical computers, can be obtained using two main approaches 1) residue number system1,2 and 2) redundant number representations3,4. In fact using of both approaches it is possible to build totally parallel adders operating by symbolic substitution (SS)2,5–7 and in constant time (the adding time is independent of the length of the operand digit strings, N). Using a residue number system, the size of the SS Truth Tables required for the carry-free addition heavily increases with numerical range involved1,2, and these tables depend on the digit position. On the contrary, additions of redundant numbers can be performed in constant time by small SS Truth Tables which are independent of the digit positions.


Truth Table Binary Number Optical Computer Residue Number System Symbolic Substitution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    H. L. Garner, “The residue number system”, IRE Trans. Electron. Comput. EC-8, 140–147 (1959)CrossRefGoogle Scholar
  2. 2.
    C. C. Guest, T. K. Gaylord, “Truth-table look-up optical processing utilizing binary and residue arithmetic”, Appl. Opt. 19, 1201–1207 (1980)CrossRefGoogle Scholar
  3. 3.
    A. Avizienis, “Signed-digit number representations for fast parallel arithmetic&”, IRE Trans. Electron. Comput. EC-10, 389–400 (1961)MathSciNetCrossRefGoogle Scholar
  4. 4.
    G. A. De Biase, A. Massini, “Redundant binary number representation for an inherently parallel arithmetic on optical computers”, Appl. Opt., 32, 659–664 (1993)CrossRefGoogle Scholar
  5. 5.
    K.-H. Brenner, “New implementation of symbolic substitution logic”, Appl. Opt. 25, 3061–3064 (1986)CrossRefGoogle Scholar
  6. 6.
    K.-H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution”, Appl. Opt. 25, 3054–3060 (1986)CrossRefGoogle Scholar
  7. 7.
    M. M. Mirsalehi, T. K. Gaylord, “Truth-table look-up parallel data processing using an optical content addressable memory”, Appl. Opt. 25, 2277–2283 (1986)CrossRefGoogle Scholar
  8. 8.
    R. P. Bocker, B. L. Drake, M. E. Lasher, T. B. Henderson, “Modified-signed addition and subtraction using optical symbolic substitution”, Appl. Opt. 25, 2456–2457 (1986)CrossRefGoogle Scholar
  9. 9.
    Y. Li, G. Eichmann, “Conditional symbolic modified signed-digit arithmetic using optical content-addressable memory logic elements”, Appl. Opt. 26, 2328–2333 (1987)CrossRefGoogle Scholar
  10. 10.
    A. K. Cherri, M. A. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution”, Appl. Opt. 27, 3824–3827 (1988)CrossRefGoogle Scholar
  11. 11.
    A. A. S. Awwal, M. N. Islam, M. A. Karim, “Modified-signed digit trinary arithmetic by using optical symbolic substitution”, Appl. Opt. 31, 1687–1694 (1992)CrossRefGoogle Scholar
  12. 12.
    G. A. De Biase, A. Massini, “High efficiency redundant binary number representations for a parallel arithmetic on optical computers”, Optics & Laser Technology, Special Issue on Optical Computing (in press)Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Giuseppe A. De Biase
    • 1
  • Annalisa Massini
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità di Roma la SapienzaRomaItaly

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