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  1. A. Avizienis, “Signed-Digit Number Representations for Fast Parallel Arithmetic,” IRE Trans. Electron. Comput. EC-10, 389 (1961).
    [CrossRef]
  2. N. Takagi, H. Yasuura, S. Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Trans. Comput. COM-34, 789 (1985).
    [CrossRef]
  3. B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
    [CrossRef]
  4. M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).
  5. A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. 83CH1880-4 (1983), p. 13.
    [CrossRef]
  6. K.-H. Brenner, A. Huang, “An Optical Processor Based on Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Comptuing (Optical Society of America, Washington, DC, 1985), paper WA4.

1986

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).

1985

N. Takagi, H. Yasuura, S. Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Trans. Comput. COM-34, 789 (1985).
[CrossRef]

1961

A. Avizienis, “Signed-Digit Number Representations for Fast Parallel Arithmetic,” IRE Trans. Electron. Comput. EC-10, 389 (1961).
[CrossRef]

Avizienis, A.

A. Avizienis, “Signed-Digit Number Representations for Fast Parallel Arithmetic,” IRE Trans. Electron. Comput. EC-10, 389 (1961).
[CrossRef]

Bocker, R. P.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).

Brenner, K.-H.

K.-H. Brenner, A. Huang, “An Optical Processor Based on Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Comptuing (Optical Society of America, Washington, DC, 1985), paper WA4.

Drake, B. L.

M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

Henderson, T. B.

M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).

Huang, A.

A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. 83CH1880-4 (1983), p. 13.
[CrossRef]

K.-H. Brenner, A. Huang, “An Optical Processor Based on Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Comptuing (Optical Society of America, Washington, DC, 1985), paper WA4.

Lasher, M. E.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).

Miceli, W. J.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

Patterson, R. H.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

Takagi, N.

N. Takagi, H. Yasuura, S. Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Trans. Comput. COM-34, 789 (1985).
[CrossRef]

Yajima, S.

N. Takagi, H. Yasuura, S. Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Trans. Comput. COM-34, 789 (1985).
[CrossRef]

Yasuura, H.

N. Takagi, H. Yasuura, S. Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Trans. Comput. COM-34, 789 (1985).
[CrossRef]

IEEE Trans. Comput.

N. Takagi, H. Yasuura, S. Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Trans. Comput. COM-34, 789 (1985).
[CrossRef]

IRE Trans. Electron. Comput.

A. Avizienis, “Signed-Digit Number Representations for Fast Parallel Arithmetic,” IRE Trans. Electron. Comput. EC-10, 389 (1961).
[CrossRef]

Opt. Eng.

B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986).
[CrossRef]

Proc. Soc. Photo-Opt. lustrum. Eng.

M. E. Lasher, T. B. Henderson, B. L. Drake, R. P. Bocker, “Encoding Schemes for a Digital Optical Multiplier Using the Modified Signed-Digit Number Representation,” Proc. Soc. Photo-Opt. lustrum. Eng. 639, 000 (1986).

Other

A. Huang, “Parallel Algorithms for Optical Digital Computers,” in Proceedings, IEEE Tenth International Optical Computing Conference, IEEE Catalog No. 83CH1880-4 (1983), p. 13.
[CrossRef]

K.-H. Brenner, A. Huang, “An Optical Processor Based on Symbolic Substitution,” in Technical Digest, Topical Meeting on Optical Comptuing (Optical Society of America, Washington, DC, 1985), paper WA4.

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Tables (1)

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Table I Modified Signed-Digit Symbolic Substitution Rules

Equations (2)

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10 1 ¯ 1 ¯ 1010 1 ¯ 01 1 ¯ + 1 1 ¯ 1 ¯ 100 1 ¯ 10110 = 01 1 ¯ 001 1 ¯ 00100 1 ¯ 1 ( 1433 10 ) + ( 758 10 ) = ( 2191 10 ) 10 1 ¯ 1 ¯ 1010 1 ¯ 01 1 ¯ augend 1 1 ¯ 1 ¯ 100 1 ¯ 10110 addend Step 1 : 1 1 ¯ 1 ¯ 01001 1 ¯ 11 1 ¯ ϕ ϕ 0100 1 ¯ 00 1 ¯ 1 1 ¯ 01 Step 2 : 00000000 1 ¯ 1000 ϕ ϕ 1 1 ¯ 001 1 ¯ 01000 1 ¯ 1 Step 3 : 01 1 ¯ 001 1 ¯ 00100 1 ¯ 1 final answer 0 1 ¯ 100 1 ¯ 100 1 ¯ 001 1 ¯ complement of answer .
1 1 ¯ 1 ¯ 100 1 ¯ 10110 - 10 1 ¯ 1 ¯ 1010 1 ¯ 01 1 ¯ = 00 1 ¯ 11 1 ¯ 1 1 ¯ 100 1 ¯ 1 1 ¯ ( 758 10 ) - ( 1433 10 ) = ( - 675 10 ) 1 1 ¯ 1 ¯ 100 1 ¯ 10110 minuend 10 1 ¯ 1 ¯ 1010 1 ¯ 01 1 ¯ subtrahend Step 1 : 1 1 ¯ 1 ¯ 100 1 ¯ 10110 augend 1 ¯ 011 1 ¯ 0 1 ¯ 010 1 ¯ 1 addend Step 2 : 0 1 ¯ 01 1 ¯ 0 1 ¯ 11101 ϕ ϕ 0100100 1 ¯ 1 ¯ 1 ¯ 0 1 ¯ Step 3 : 0000000000000 ϕ ϕ 0 1 ¯ 11 1 ¯ 1 1 ¯ 100 1 ¯ 1 1 ¯ Step 4 : 00 1 ¯ 11 1 ¯ 1 1 ¯ 100 1 ¯ 1 1 ¯ final answer 001 1 ¯ 1 ¯ 1 1 ¯ 1 1 ¯ 001 1 ¯ 1 complement of answer .

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