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]

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]

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]

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]

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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

[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]

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]

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

[CrossRef]
[PubMed]

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

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. 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]

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, “Symbolic substitution based operations using
holograms: multiplication and histogram equalization,”
Opt. Eng. 28, 638–644
(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]

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. 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).

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]

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]

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).