Abstract

A simplified arithmetic digitwise positional operation is proposed that uses only moduli 2 and 5 of the residue number system.

© 1990 Optical Society of America

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References

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  1. A. P. Goutzoulis, “Complexity of Residue Position-Coded Lookup Table Array Processors,” Appl. Opt. 2823 (1987).
  2. 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 (1986).
    [CrossRef] [PubMed]
  3. S. Mukhopadhyay, A. Basuray, A. K. Datta, “New Coding Scheme for Addition and Subtraction Using the Modified Signed-Digit Number Representation in Optical Computation,” Appl. Opt. 27, 1375 (1988).
    [CrossRef] [PubMed]
  4. A. P. Goutzoulis, E. C. Malarkey, D. K. Davies, J. C. Bradley, P. R. Beaudet, “Optical Processing with Residue LED/LD Lookup Tables,” Appl. Opt. 27, 1674 (1988).
    [CrossRef] [PubMed]
  5. C. D. Capps, R. A. Falk, T. L. Houk, “Optical Arithmetic/Logic Unit Based on Residue Arithmetic and Symbolic Substitution,” Appl. Opt. 27, 1682 (1988).
    [CrossRef] [PubMed]
  6. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, “Optical Computation Using Residue Arithmetic,” Appl. Opt. 18, 149 (1979).
    [CrossRef] [PubMed]
  7. A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).
  8. C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.
  9. M. M. Mirsalehi, J. Shamir, H. J. Caulfield, “Residue Arithmetic Processor Utilizing Optical Fredkin Gates,” Appl. Opt. 26, 3940 (1987).
    [CrossRef] [PubMed]
  10. N. S. Szabo, R. I. Tanaka, Residue Arithmetic and its Applications to Computer Technology (McGraw-Hill, New York, 1967).
  11. M. A. Maclean, D. Aspinall, “Decimal Adder Using Stored Addition Table,” Proc. IEE 105B(20), 129 (1958).

1988 (3)

1987 (3)

M. M. Mirsalehi, J. Shamir, H. J. Caulfield, “Residue Arithmetic Processor Utilizing Optical Fredkin Gates,” Appl. Opt. 26, 3940 (1987).
[CrossRef] [PubMed]

A. P. Goutzoulis, “Complexity of Residue Position-Coded Lookup Table Array Processors,” Appl. Opt. 2823 (1987).

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

1986 (1)

1979 (1)

1958 (1)

M. A. Maclean, D. Aspinall, “Decimal Adder Using Stored Addition Table,” Proc. IEE 105B(20), 129 (1958).

Aspinall, D.

M. A. Maclean, D. Aspinall, “Decimal Adder Using Stored Addition Table,” Proc. IEE 105B(20), 129 (1958).

Basuray, A.

Beaudet, P. R.

Bocker, R. P.

Bradley, J. C.

Capps, C.

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

Capps, C. D.

Caulfield, H. J.

Datta, A. K.

Davies, D. K.

A. P. Goutzoulis, E. C. Malarkey, D. K. Davies, J. C. Bradley, P. R. Beaudet, “Optical Processing with Residue LED/LD Lookup Tables,” Appl. Opt. 27, 1674 (1988).
[CrossRef] [PubMed]

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

Drake, B. L.

Falk, R.

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

Falk, R. A.

Goodman, J. W.

Goutzoulis, A. P.

A. P. Goutzoulis, E. C. Malarkey, D. K. Davies, J. C. Bradley, P. R. Beaudet, “Optical Processing with Residue LED/LD Lookup Tables,” Appl. Opt. 27, 1674 (1988).
[CrossRef] [PubMed]

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

A. P. Goutzoulis, “Complexity of Residue Position-Coded Lookup Table Array Processors,” Appl. Opt. 2823 (1987).

Henderson, T. B.

Houk, T.

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

Houk, T. L.

Huang, A.

Ishihara, S.

Lasher, M. E.

Maclean, M. A.

M. A. Maclean, D. Aspinall, “Decimal Adder Using Stored Addition Table,” Proc. IEE 105B(20), 129 (1958).

Malarkey, E. C.

Mirsalehi, M. M.

Mukhopadhyay, S.

Shamir, J.

Szabo, N. S.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Tanaka, R. I.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Tsunoda, Y.

Appl. Opt. (7)

Proc. IEE (1)

M. A. Maclean, D. Aspinall, “Decimal Adder Using Stored Addition Table,” Proc. IEE 105B(20), 129 (1958).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. P. Goutzoulis, D. K. Davies, “On the Characteristics of Practical Optical Residue Look-Up Table Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 827, 226 (1987).

Other (2)

C. Capps, R. Falk, T. Houk, “An Optical Arithmetic/Logic Unit Based on Residue Number Theory and Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), paper MD4.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and its Applications to Computer Technology (McGraw-Hill, New York, 1967).

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Tables (1)

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Table I Addition of Two Decimal Numbers 4568 and 7894

Equations (22)

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M = [ ( i = 1 K m i ) - 1 ] .
x m = R m ,
x m p = x n m x n - 1 m , , x 0 m ,
x m p = R n R n - 1 , , R 0 .
Q = Q n Q n - 1 , , Q 0 .
x = m [ Q n , , Q 0 ] + [ R n , , R 0 ] .
x 2 = R 2 x n R 2 x ( n - 1 ) , , R 2 x 0 ,
x 5 = R 5 x n R 5 x ( n - 1 ) , , R 5 x 0 ,
y 2 = R 2 y n R 2 y ( n - 1 ) , , R 2 y 0 ,
y 5 = R 5 y n R 5 y ( n - 1 ) , , R 5 y 0 .
x 2 + y 2 = R 2 x n + R 2 y n 2 , , R 2 n 0 + R 2 y 0 2 ,
x 5 + y 5 = R 5 x n + R 5 y n 5 , , R 5 x 0 + R 5 y 0 5 .
Q 5 x = Q 5 x n , , Q 5 x 0 ;
Q 5 y = Q 5 y n , , Q 5 y 0 .
Q 5 x y = Q 5 x y n , , Q 5 x y 0 .
Q add = ( Q 5 x + Q 5 y + Q 5 x y ) = ( Q 5 x n + Q 5 y n + Q 5 x y n ) , , ( Q 5 x 0 + Q 5 y 0 + Q 5 x y 0 ) .
Q add 2 = Q x y n 2 , , Q x y 0 2 ,
x + y 2 = 0 + Q x y n 2 2 , R 2 x n + R 2 y n 2 + Q x y ( n - 1 ) 2 2 , , R 2 x 1 + R 2 y 1 2 + Q x y 0 2 2 , R 2 x 0 + R 2 y 0 2 + 0 2 , ,
x + y 5 = 0 + Q x y n 2 5 , R 5 x n + R 5 y n 5 + Q x y ( n - 1 ) 2 5 , , R 5 x 1 + R 5 y 1 5 + Q x y 0 2 5 , R 5 x 0 + R 5 y 0 5 + 0 5 , .
x + y n 2 = R n 2 + 2 P , P = 1 , 2 , 3 , ,
x + y n 5 = R n 5 + 2 Q , Q = 1 , 2 , 3 , ,
x + y = 12 , 462.

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