G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit
multiplication and its use for matrix-vector operation,”
Optik (Stuttgart/Weimar) 107, 165–172
(1998).

A. K. Cherri, M. K. Habib, M. S. Alam, “Optoelectronic recoded and nonrecoded
trinary signed-digit adder using optical correlation,”
Appl. Opt. 37, 2153–2163
(1998).

[CrossRef]

A. K. Cherri, N. I. Khachab, E. H. Ismail, “One-step optical trinary signed-digit
arithmetic using redundant bit representations,”
Opt. Laser Technol. 29, 281–290
(1997).

[CrossRef]

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit
arithmetic and its optical implementation,” Opt.
Commun. 173, 389–396
(1997).

[CrossRef]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical higher-order symbolic
recognition,” Appl. Opt. 29, 2135–2147
(1996).

[CrossRef]

G. Li, L. Liu, L. Shao, Y. Yin, “Optical negabinary addition with
higher-order substitution rules,” Opt.
Commun. 129, 323–330
(1996).

[CrossRef]

A. K. Cherri, N. I. Khachab, “Canonical quaternary signed-digit arithmetic
using optoelectronics symbolic substitution,” Opt.
Laser Technol. 28, 397–403
(1996).

[CrossRef]

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary
signed-digit arithmetic using a shared content-addressable
memory,” Opt. Eng. 35, 1141–1149
(1996).

[CrossRef]

G. A. De Biase, A. Massini, “High efficiency redundant binary number
representations for parallel arithmetic on optical
computers,” Opt. Laser Technol. 26, 219–224
(1994).

[CrossRef]

H. Huang, M. Itoh, T. Yatagai, “Modified signed-digit arithmetic based on
redundant bit representation,” Appl. Opt. 33, 6146–6156
(1994).

[CrossRef]
[PubMed]

B. Ha, Y. Li, “Parallel modified signed-digit arithmetic
using an optoelectronic shared content-addressable-memory
processor,” Appl. Opt. 33, 3647–3662
(1994).

[CrossRef]
[PubMed]

A. A. S. Awwal, M. N. Islam, M. A. Karim, “Modified signed-digit trinary arithmetic by
using symbolic substitution,” Appl. Opt. 31, 1687–1694
(1994).

[CrossRef]

D. P. Casasent, P. Woodford, “Symbolic substitution modified signed-digit
optical adder,” Appl. Opt. 33, 1498–1506
(1994).

[CrossRef]
[PubMed]

M. S. Alam, “Parallel optical computing using recoded
trinary signed-digit numbers,” Appl. Opt. 33, 4392–4397
(1994).

[CrossRef]
[PubMed]

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[CrossRef]
[PubMed]

K. Al-Ghoneim, D. P. Casasent, “High-accuracy pipelined iterative-tree
optical multiplication,” Appl. Opt. 33, 4392–4397
(1994).

[CrossRef]

E. Botha, J. Richards, D. P. Casassent, “Optical laboratory morphological inspection
processor,” Appl. Opt. 28, 5342–5350
(1989).

[CrossRef]
[PubMed]

A. K. Cherri, M. A. Karim, “Symbolic substitution based operations using
holograms: multiplication and histogram equalization,”
Opt. Eng. 28, 638–644
(1989).

[CrossRef]

A. K. Cherri, M. A. Karim, “Edge detection using symbolic
substitution,” Opt. Commun. 74, 10–14
(1989).

[CrossRef]

A. K. Cherri, M. A. Karim, “Optical symbolic substitution: edge
detection using Prewitt, Sobel, and Roberts operators,”
Appl. Opt. 28, 4644–4648
(1989).

[CrossRef]
[PubMed]

Y. Li, 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]

L. Liu, “Optoelectronics implementation of
mathmatical morphology,” Opt. Lett. 14, 482–485
(1989).

[CrossRef]
[PubMed]

D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on
symbolic substitution,” Opt. Eng. 28, 425–433
(1989).

[CrossRef]

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

[CrossRef]
[PubMed]

A. P. Gautzouilis, E. C. Malarkey, D. K. Davies, J. C. Bradley, P. R. Beaudet, “Optical processing with residue LED/LD
lookup tables,” Appl. Opt. 27, 1674–1681
(1988).

[CrossRef]

A. Avizienis, “Signed-digit number representations for fast
parallel arithmetic,” IRE Trans. Electronic
Computers, EC-10,
389–400
(1961).

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary
signed-digit arithmetic using a shared content-addressable
memory,” Opt. Eng. 35, 1141–1149
(1996).

[CrossRef]

A. K. Cherri, M. K. Habib, M. S. Alam, “Optoelectronic recoded and nonrecoded
trinary signed-digit adder using optical correlation,”
Appl. Opt. 37, 2153–2163
(1998).

[CrossRef]

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary
signed-digit arithmetic using a shared content-addressable
memory,” Opt. Eng. 35, 1141–1149
(1996).

[CrossRef]

M. S. Alam, “Parallel optical computing using recoded
trinary signed-digit numbers,” Appl. Opt. 33, 4392–4397
(1994).

[CrossRef]
[PubMed]

A. Avizienis, “Signed-digit number representations for fast
parallel arithmetic,” IRE Trans. Electronic
Computers, EC-10,
389–400
(1961).

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[CrossRef]
[PubMed]

K. Al-Ghoneim, D. P. Casasent, “High-accuracy pipelined iterative-tree
optical multiplication,” Appl. Opt. 33, 4392–4397
(1994).

[CrossRef]

D. P. Casasent, P. Woodford, “Symbolic substitution modified signed-digit
optical adder,” Appl. Opt. 33, 1498–1506
(1994).

[CrossRef]
[PubMed]

D. P. Casasent, E. C. Botha, “Optical correlator production system neural
net,” Appl. Opt. 31, 1030–1040
(1992).

[CrossRef]
[PubMed]

D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on
symbolic substitution,” Opt. Eng. 28, 425–433
(1989).

[CrossRef]

D. P. Casasent, R. Sturgill, “Optical hit-or-miss morphological transforms
for ATR,” in Applications of Digital Image
Processing XII, J. Neffs, ed., Proc. SPIE1153, 500–510
(1989).

[CrossRef]

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary
signed-digit arithmetic using a shared content-addressable
memory,” Opt. Eng. 35, 1141–1149
(1996).

[CrossRef]

G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit
multiplication and its use for matrix-vector operation,”
Optik (Stuttgart/Weimar) 107, 165–172
(1998).

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit
arithmetic and its optical implementation,” Opt.
Commun. 173, 389–396
(1997).

[CrossRef]

A. K. Cherri, M. K. Habib, M. S. Alam, “Optoelectronic recoded and nonrecoded
trinary signed-digit adder using optical correlation,”
Appl. Opt. 37, 2153–2163
(1998).

[CrossRef]

A. K. Cherri, N. I. Khachab, E. H. Ismail, “One-step optical trinary signed-digit
arithmetic using redundant bit representations,”
Opt. Laser Technol. 29, 281–290
(1997).

[CrossRef]

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary
signed-digit arithmetic using a shared content-addressable
memory,” Opt. Eng. 35, 1141–1149
(1996).

[CrossRef]

A. K. Cherri, N. I. Khachab, “Canonical quaternary signed-digit arithmetic
using optoelectronics symbolic substitution,” Opt.
Laser Technol. 28, 397–403
(1996).

[CrossRef]

A. K. Cherri, M. A. Karim, “Symbolic substitution based operations using
holograms: multiplication and histogram equalization,”
Opt. Eng. 28, 638–644
(1989).

[CrossRef]

A. K. Cherri, M. A. Karim, “Edge detection using symbolic
substitution,” Opt. Commun. 74, 10–14
(1989).

[CrossRef]

A. K. Cherri, M. A. Karim, “Optical symbolic substitution: edge
detection using Prewitt, Sobel, and Roberts operators,”
Appl. Opt. 28, 4644–4648
(1989).

[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]

G. A. De Biase, A. Massini, “High efficiency redundant binary number
representations for parallel arithmetic on optical
computers,” Opt. Laser Technol. 26, 219–224
(1994).

[CrossRef]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical higher-order symbolic
recognition,” Appl. Opt. 29, 2135–2147
(1996).

[CrossRef]

Y. Li, 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]

A. Huang, “Parallel algorithms for optical digital
computers,” in Proceedings of the Tenth
International Optical Computing Conference, S. Horvitz, ed. (IEEE Computer Society,
Los Alamitos, Calif., 1983), pp.
13–17.

[CrossRef]

K. Hwang, D. K. Panda, “High-radix symbolic substitution and
superposition techniques for optical matrix algebraic
computations,” Opt. Eng. 31, 2422–2433
(1992).

[CrossRef]

K. Hwang, Computer Arithmetic Principles: Architecture and
Design (Wiley, New
York, 1979).

A. K. Cherri, N. I. Khachab, E. H. Ismail, “One-step optical trinary signed-digit
arithmetic using redundant bit representations,”
Opt. Laser Technol. 29, 281–290
(1997).

[CrossRef]

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit
arithmetic and its optical implementation,” Opt.
Commun. 173, 389–396
(1997).

[CrossRef]

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

A. A. S. Awwal, M. N. Islam, M. A. Karim, “Modified signed-digit trinary arithmetic by
using symbolic substitution,” Appl. Opt. 31, 1687–1694
(1994).

[CrossRef]

A. K. Cherri, M. A. Karim, “Optical symbolic substitution: edge
detection using Prewitt, Sobel, and Roberts operators,”
Appl. Opt. 28, 4644–4648
(1989).

[CrossRef]
[PubMed]

A. K. Cherri, M. A. Karim, “Symbolic substitution based operations using
holograms: multiplication and histogram equalization,”
Opt. Eng. 28, 638–644
(1989).

[CrossRef]

A. K. Cherri, M. A. Karim, “Edge detection using symbolic
substitution,” Opt. Commun. 74, 10–14
(1989).

[CrossRef]

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

[CrossRef]
[PubMed]

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

A. K. Cherri, N. I. Khachab, E. H. Ismail, “One-step optical trinary signed-digit
arithmetic using redundant bit representations,”
Opt. Laser Technol. 29, 281–290
(1997).

[CrossRef]

A. K. Cherri, N. I. Khachab, “Canonical quaternary signed-digit arithmetic
using optoelectronics symbolic substitution,” Opt.
Laser Technol. 28, 397–403
(1996).

[CrossRef]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical higher-order symbolic
recognition,” Appl. Opt. 29, 2135–2147
(1996).

[CrossRef]

Y. Li, 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]

G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit
multiplication and its use for matrix-vector operation,”
Optik (Stuttgart/Weimar) 107, 165–172
(1998).

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit
arithmetic and its optical implementation,” Opt.
Commun. 173, 389–396
(1997).

[CrossRef]

G. Li, L. Liu, L. Shao, Y. Yin, “Optical negabinary addition with
higher-order substitution rules,” Opt.
Commun. 129, 323–330
(1996).

[CrossRef]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical higher-order symbolic
recognition,” Appl. Opt. 29, 2135–2147
(1996).

[CrossRef]

B. Ha, Y. Li, “Parallel modified signed-digit arithmetic
using an optoelectronic shared content-addressable-memory
processor,” Appl. Opt. 33, 3647–3662
(1994).

[CrossRef]
[PubMed]

Y. Li, 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]

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[CrossRef]
[PubMed]

G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit
multiplication and its use for matrix-vector operation,”
Optik (Stuttgart/Weimar) 107, 165–172
(1998).

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit
arithmetic and its optical implementation,” Opt.
Commun. 173, 389–396
(1997).

[CrossRef]

G. Li, L. Liu, L. Shao, Y. Yin, “Optical negabinary addition with
higher-order substitution rules,” Opt.
Commun. 129, 323–330
(1996).

[CrossRef]

L. Liu, “Optoelectronics implementation of
mathmatical morphology,” Opt. Lett. 14, 482–485
(1989).

[CrossRef]
[PubMed]

G. A. De Biase, A. Massini, “High efficiency redundant binary number
representations for parallel arithmetic on optical
computers,” Opt. Laser Technol. 26, 219–224
(1994).

[CrossRef]

K. Hwang, D. K. Panda, “High-radix symbolic substitution and
superposition techniques for optical matrix algebraic
computations,” Opt. Eng. 31, 2422–2433
(1992).

[CrossRef]

G. Li, L. Liu, L. Shao, Y. Yin, “Optical negabinary addition with
higher-order substitution rules,” Opt.
Commun. 129, 323–330
(1996).

[CrossRef]

D. P. Casasent, R. Sturgill, “Optical hit-or-miss morphological transforms
for ATR,” in Applications of Digital Image
Processing XII, J. Neffs, ed., Proc. SPIE1153, 500–510
(1989).

[CrossRef]

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[CrossRef]
[PubMed]

G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit
multiplication and its use for matrix-vector operation,”
Optik (Stuttgart/Weimar) 107, 165–172
(1998).

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[CrossRef]
[PubMed]

G. Li, L. Liu, L. Shao, Y. Yin, “Optical negabinary addition with
higher-order substitution rules,” Opt.
Commun. 129, 323–330
(1996).

[CrossRef]

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[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]

S. Zhou, S. Campbell, W. Wu, P. Yeh, H.-K. Liu, “Modified signed-digit arithmetic for
multi-input digital computing,” Appl.
Opt. 33, 1507–1516
(1994).

[CrossRef]
[PubMed]

G. Eichmann, A. Kostrzewski, D. H. Kim, Y. Li, “Optical higher-order symbolic
recognition,” Appl. Opt. 29, 2135–2147
(1996).

[CrossRef]

H. Huang, M. Itoh, T. Yatagai, “Modified signed-digit arithmetic based on
redundant bit representation,” Appl. Opt. 33, 6146–6156
(1994).

[CrossRef]
[PubMed]

B. Ha, Y. Li, “Parallel modified signed-digit arithmetic
using an optoelectronic shared content-addressable-memory
processor,” Appl. Opt. 33, 3647–3662
(1994).

[CrossRef]
[PubMed]

A. P. Gautzouilis, E. C. Malarkey, D. K. Davies, J. C. Bradley, P. R. Beaudet, “Optical processing with residue LED/LD
lookup tables,” Appl. Opt. 27, 1674–1681
(1988).

[CrossRef]

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]

A. K. Cherri, M. K. Habib, M. S. Alam, “Optoelectronic recoded and nonrecoded
trinary signed-digit adder using optical correlation,”
Appl. Opt. 37, 2153–2163
(1998).

[CrossRef]

A. A. S. Awwal, M. N. Islam, M. A. Karim, “Modified signed-digit trinary arithmetic by
using symbolic substitution,” Appl. Opt. 31, 1687–1694
(1994).

[CrossRef]

D. P. Casasent, P. Woodford, “Symbolic substitution modified signed-digit
optical adder,” Appl. Opt. 33, 1498–1506
(1994).

[CrossRef]
[PubMed]

M. S. Alam, “Parallel optical computing using recoded
trinary signed-digit numbers,” Appl. Opt. 33, 4392–4397
(1994).

[CrossRef]
[PubMed]

D. P. Casasent, E. C. Botha, “Optical correlator production system neural
net,” Appl. Opt. 31, 1030–1040
(1992).

[CrossRef]
[PubMed]

E. Botha, J. Richards, D. P. Casassent, “Optical laboratory morphological inspection
processor,” Appl. Opt. 28, 5342–5350
(1989).

[CrossRef]
[PubMed]

K. Al-Ghoneim, D. P. Casasent, “High-accuracy pipelined iterative-tree
optical multiplication,” Appl. Opt. 33, 4392–4397
(1994).

[CrossRef]

A. K. Cherri, M. A. Karim, “Optical symbolic substitution: edge
detection using Prewitt, Sobel, and Roberts operators,”
Appl. Opt. 28, 4644–4648
(1989).

[CrossRef]
[PubMed]

A. Louri, “Throughput enhancement for optical symbolic
substitution systems,” Appl. Opt. 29, 2979–2980
(1990).

[CrossRef]
[PubMed]

A. Avizienis, “Signed-digit number representations for fast
parallel arithmetic,” IRE Trans. Electronic
Computers, EC-10,
389–400
(1961).

G. Li, L. Liu, L. Shao, Y. Yin, “Optical negabinary addition with
higher-order substitution rules,” Opt.
Commun. 129, 323–330
(1996).

[CrossRef]

G. Li, L. Liu, H. Cheng, H. Jing, “Simplified quaternary signed-digit
arithmetic and its optical implementation,” Opt.
Commun. 173, 389–396
(1997).

[CrossRef]

A. K. Cherri, N. I. Khachab, “Canonical quaternary signed-digit arithmetic
using optoelectronics symbolic substitution,” Opt.
Laser Technol. 28, 397–403
(1996).

[CrossRef]

A. K. Cherri, M. A. Karim, “Edge detection using symbolic
substitution,” Opt. Commun. 74, 10–14
(1989).

[CrossRef]

A. K. Cherri, M. A. Karim, “Symbolic substitution based operations using
holograms: multiplication and histogram equalization,”
Opt. Eng. 28, 638–644
(1989).

[CrossRef]

D. P. Casasent, E. C. Botha, “Multifunctional optical processor based on
symbolic substitution,” Opt. Eng. 28, 425–433
(1989).

[CrossRef]

K. Hwang, D. K. Panda, “High-radix symbolic substitution and
superposition techniques for optical matrix algebraic
computations,” Opt. Eng. 31, 2422–2433
(1992).

[CrossRef]

M. S. Alam, Y. Ahuja, A. K. Cherri, A. Chatterjea, “Symmetrically recoded quaternary
signed-digit arithmetic using a shared content-addressable
memory,” Opt. Eng. 35, 1141–1149
(1996).

[CrossRef]

G. A. De Biase, A. Massini, “High efficiency redundant binary number
representations for parallel arithmetic on optical
computers,” Opt. Laser Technol. 26, 219–224
(1994).

[CrossRef]

A. K. Cherri, N. I. Khachab, E. H. Ismail, “One-step optical trinary signed-digit
arithmetic using redundant bit representations,”
Opt. Laser Technol. 29, 281–290
(1997).

[CrossRef]

G. Li, L. Liu, H. Cheng, X. Yan, “Parallel optical quaternary signed-digit
multiplication and its use for matrix-vector operation,”
Optik (Stuttgart/Weimar) 107, 165–172
(1998).

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

K. Hwang, Computer Arithmetic Principles: Architecture and
Design (Wiley, New
York, 1979).

A. Huang, “Parallel algorithms for optical digital
computers,” in Proceedings of the Tenth
International Optical Computing Conference, S. Horvitz, ed. (IEEE Computer Society,
Los Alamitos, Calif., 1983), pp.
13–17.

[CrossRef]

D. P. Casasent, R. Sturgill, “Optical hit-or-miss morphological transforms
for ATR,” in Applications of Digital Image
Processing XII, J. Neffs, ed., Proc. SPIE1153, 500–510
(1989).

[CrossRef]