Abstract
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.
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References
H. L. Garner, “The residue number system”, IRE Trans. Electron. Comput. EC-8, 140–147 (1959)
C. C. Guest, T. K. Gaylord, “Truth-table look-up optical processing utilizing binary and residue arithmetic”, Appl. Opt. 19, 1201–1207 (1980)
A. Avizienis, “Signed-digit number representations for fast parallel arithmetic&”, IRE Trans. Electron. Comput. EC-10, 389–400 (1961)
G. A. De Biase, A. Massini, “Redundant binary number representation for an inherently parallel arithmetic on optical computers”, Appl. Opt., 32, 659–664 (1993)
K.-H. Brenner, “New implementation of symbolic substitution logic”, Appl. Opt. 25, 3061–3064 (1986)
K.-H. Brenner, A. Huang, N. Streibl, “Digital optical computing with symbolic substitution”, Appl. Opt. 25, 3054–3060 (1986)
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)
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)
Y. Li, G. Eichmann, “Conditional symbolic modified signed-digit arithmetic using optical content-addressable memory logic elements”, Appl. Opt. 26, 2328–2333 (1987)
A. K. Cherri, M. A. Karim, “Modified-signed digit arithmetic using an efficient symbolic substitution”, Appl. Opt. 27, 3824–3827 (1988)
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)
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)
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© 1995 Springer Science+Business Media New York
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De Biase, G.A., Massini, A. (1995). Parallel Arithmetic on Optical Computers by Redundant Binary Number Representations. In: Lampropoulos, G.A., Chrostowski, J., Measures, R.M. (eds) Applications of Photonic Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9247-8_20
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DOI: https://doi.org/10.1007/978-1-4757-9247-8_20
Publisher Name: Springer, Boston, MA
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