Abstract

A 2 × 2 bit multiplier is designed by the use of a butterfly interconnection network. The butterfly topology is also used to design a sequential flip-flop and a multibit parallel-in parallel-out shift register.

© 1994 Optical Society of America

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References

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  1. J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
    [CrossRef]
  2. H. M Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985), Chap. 2, p. 21.
  3. J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
    [CrossRef]
  4. A. L. Lentine, S. J Hinterlong, T. J. Cloonan, F. B. McCormick, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, R. F. Kopf, J. M. Kuo, “Quantum well optical tri-state devices,” Appl. Opt. 29, 1157–1160 (1990).
    [CrossRef] [PubMed]
  5. A. Guha, J. Bristow, C. Sullivan, A. Husain, “Optical interconnections for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
    [CrossRef] [PubMed]
  6. M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
    [CrossRef] [PubMed]
  7. W. Shudong, S. Qiwang, A. Mayers, D. A. Gregory, F. T. S. Yu, “Reconfigurable interconnections using photorefractive holograms,” Appl. Opt. 29, 1118–1125 (1990).
    [CrossRef]
  8. T. J. Cloonan, F. B. McCormick, “Photonic switching applications of 2-D and 3-D crossover networks based on 2-input, 2-output switching nodes,” Appl. Opt. 30, 2309–2323 (1991).
    [CrossRef] [PubMed]
  9. A. W. Lohmann, W. Stork, G. Stucke, “Optical perfect shuffle,” Appl. Opt. 25, 1530–1531 (1986).
    [CrossRef] [PubMed]
  10. M. S. Alam, M. A. Karim, “Programmable optical perfect shuffle interconnection network using Fredkin gates,” Microwave Opt. Technol. Lett. 5, 330–333 (1992).
    [CrossRef]
  11. S. H. Lin, T. F. Krile, J. F. Walkup, “Two-dimensional optical Clos interconnection network and its uses,” Appl. Opt. 27, 1734–1741 (1988).
    [CrossRef] [PubMed]
  12. D. G. Sun, Z. H. Weng, “Butterfly interconnection implementation for n-bit parallel ripple carry full adder,” Appl. Opt. 30, 1781–1785 (1991).
    [CrossRef] [PubMed]
  13. K. H. Brenner, A. Huang, “Optical implementations of the perfect shuffle interconnections,” Appl. Opt. 27, 135–137 (1988).
    [CrossRef] [PubMed]
  14. M. Murdocca, “Connection routing for micro-optic system,” Appl. Opt. 29, 1106–1110 (1990).
    [CrossRef] [PubMed]
  15. P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 72, 20–25 (1984).
  16. D. Psaltis, R. A. Athale, “High accuracy computation with linear analog optical systems: a critical study,” Appl. Opt. 25, 3071–3077 (1986).
    [CrossRef] [PubMed]
  17. M. A. Karim, “Smart quasi-serial post processor for optical systolic systems,” Appl. Opt. 30, 910–912 (1991).
    [CrossRef] [PubMed]
  18. A. K. Cherri, M. A. Karim, “Symbolic-substitution-based operations using holograms: multiplication and histogram equalization,” Opt. Eng. 28, 638–642 (1989).
  19. M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992), Chap. 11, p. 292.
  20. T. Sakano, K. Noguchi, T. Matsumoto, “Optical limits for spatial interconnection networks using 2-D optical array devices,” Appl. Opt. 29, 1094–1100 (1990).
    [CrossRef] [PubMed]
  21. F. B. McCormick, M. E. Prise, “Optical circuitry for free-space interconnections,” Appl. Opt. 29, 2013–2018 (1990).
    [CrossRef] [PubMed]
  22. T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
    [CrossRef]
  23. J. Jahns, “Optical implementation of the Banyan network,” Opt. Commun. 76, 321–324 (1990).
    [CrossRef]

1992 (1)

M. S. Alam, M. A. Karim, “Programmable optical perfect shuffle interconnection network using Fredkin gates,” Microwave Opt. Technol. Lett. 5, 330–333 (1992).
[CrossRef]

1991 (3)

1990 (8)

1989 (1)

A. K. Cherri, M. A. Karim, “Symbolic-substitution-based operations using holograms: multiplication and histogram equalization,” Opt. Eng. 28, 638–642 (1989).

1988 (3)

1986 (2)

1985 (1)

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

1984 (2)

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
[CrossRef]

P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 72, 20–25 (1984).

Alam, M. S.

M. S. Alam, M. A. Karim, “Programmable optical perfect shuffle interconnection network using Fredkin gates,” Microwave Opt. Technol. Lett. 5, 330–333 (1992).
[CrossRef]

Athale, R.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
[CrossRef]

Athale, R. A.

Awwal, A. A. S.

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992), Chap. 11, p. 292.

Brenner, K. H.

Bristow, J.

Brubaker, J. L.

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Cherri, A. K.

A. K. Cherri, M. A. Karim, “Symbolic-substitution-based operations using holograms: multiplication and histogram equalization,” Opt. Eng. 28, 638–642 (1989).

Chirovsky, L. M. F.

Cloonan, T. J.

D’Asaro, L. A.

Gibbs, H. M

H. M Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985), Chap. 2, p. 21.

Gibbs, H. M.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
[CrossRef]

Gossard, A. C.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Gregory, D. A.

Guha, A.

Guilfoyle, P. S.

P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 72, 20–25 (1984).

Herron, M. J.

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Hinterlong, S. J

Huang, A.

Husain, A.

Jahns, J.

Jewell, J. L.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Karim, M. A.

M. S. Alam, M. A. Karim, “Programmable optical perfect shuffle interconnection network using Fredkin gates,” Microwave Opt. Technol. Lett. 5, 330–333 (1992).
[CrossRef]

M. A. Karim, “Smart quasi-serial post processor for optical systolic systems,” Appl. Opt. 30, 910–912 (1991).
[CrossRef] [PubMed]

A. K. Cherri, M. A. Karim, “Symbolic-substitution-based operations using holograms: multiplication and histogram equalization,” Opt. Eng. 28, 638–642 (1989).

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992), Chap. 11, p. 292.

Kerbis, E.

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Kopf, R. F.

Krile, T. F.

Kung, S. Y.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
[CrossRef]

Kuo, J. M.

Lee, Y. H.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Lentine, A. L.

A. L. Lentine, S. J Hinterlong, T. J. Cloonan, F. B. McCormick, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, R. F. Kopf, J. M. Kuo, “Quantum well optical tri-state devices,” Appl. Opt. 29, 1157–1160 (1990).
[CrossRef] [PubMed]

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Leonberger, F.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
[CrossRef]

Lin, S. H.

Lohmann, A. W.

Matsumoto, T.

Mayers, A.

McCormick, F. B.

Miller, D. A. B.

Murdocca, M.

Murdocca, M. J.

Noguchi, K.

Peyghambarian, N.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Prise, M. E.

Psaltis, D.

Qiwang, S.

Richards, G. W.

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Sakano, T.

Shudong, W.

Stork, W.

Streibl, N.

Stucke, G.

Sullivan, C.

Sun, D. G.

Tooley, F. A. P.

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Walkup, J. F.

Warren, M.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Weng, Z. H.

Wiegmann, W.

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

Yu, F. T. S.

Appl. Opt. (14)

A. L. Lentine, S. J Hinterlong, T. J. Cloonan, F. B. McCormick, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, R. F. Kopf, J. M. Kuo, “Quantum well optical tri-state devices,” Appl. Opt. 29, 1157–1160 (1990).
[CrossRef] [PubMed]

A. Guha, J. Bristow, C. Sullivan, A. Husain, “Optical interconnections for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
[CrossRef] [PubMed]

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
[CrossRef] [PubMed]

W. Shudong, S. Qiwang, A. Mayers, D. A. Gregory, F. T. S. Yu, “Reconfigurable interconnections using photorefractive holograms,” Appl. Opt. 29, 1118–1125 (1990).
[CrossRef]

T. J. Cloonan, F. B. McCormick, “Photonic switching applications of 2-D and 3-D crossover networks based on 2-input, 2-output switching nodes,” Appl. Opt. 30, 2309–2323 (1991).
[CrossRef] [PubMed]

A. W. Lohmann, W. Stork, G. Stucke, “Optical perfect shuffle,” Appl. Opt. 25, 1530–1531 (1986).
[CrossRef] [PubMed]

S. H. Lin, T. F. Krile, J. F. Walkup, “Two-dimensional optical Clos interconnection network and its uses,” Appl. Opt. 27, 1734–1741 (1988).
[CrossRef] [PubMed]

D. G. Sun, Z. H. Weng, “Butterfly interconnection implementation for n-bit parallel ripple carry full adder,” Appl. Opt. 30, 1781–1785 (1991).
[CrossRef] [PubMed]

K. H. Brenner, A. Huang, “Optical implementations of the perfect shuffle interconnections,” Appl. Opt. 27, 135–137 (1988).
[CrossRef] [PubMed]

M. Murdocca, “Connection routing for micro-optic system,” Appl. Opt. 29, 1106–1110 (1990).
[CrossRef] [PubMed]

D. Psaltis, R. A. Athale, “High accuracy computation with linear analog optical systems: a critical study,” Appl. Opt. 25, 3071–3077 (1986).
[CrossRef] [PubMed]

M. A. Karim, “Smart quasi-serial post processor for optical systolic systems,” Appl. Opt. 30, 910–912 (1991).
[CrossRef] [PubMed]

T. Sakano, K. Noguchi, T. Matsumoto, “Optical limits for spatial interconnection networks using 2-D optical array devices,” Appl. Opt. 29, 1094–1100 (1990).
[CrossRef] [PubMed]

F. B. McCormick, M. E. Prise, “Optical circuitry for free-space interconnections,” Appl. Opt. 29, 2013–2018 (1990).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. L. Jewell, Y. H. Lee, M. Warren, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ 82-MHz optical logic gates in a room temperature GaAs–AlGaAs multiple quantum well étalon,” Appl. Phys. Lett. 46, 918–923 (1985).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. J. Cloonan, M. J. Herron, F. A. P. Tooley, G. W. Richards, F. B. McCormick, E. Kerbis, J. L. Brubaker, A. L. Lentine, “An all-optical implementation of a 3-D crossover switching network,” IEEE Photon. Technol. Lett. 2, 438–440 (1990).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. S. Alam, M. A. Karim, “Programmable optical perfect shuffle interconnection network using Fredkin gates,” Microwave Opt. Technol. Lett. 5, 330–333 (1992).
[CrossRef]

Opt. Commun. (1)

J. Jahns, “Optical implementation of the Banyan network,” Opt. Commun. 76, 321–324 (1990).
[CrossRef]

Opt. Eng. (2)

A. K. Cherri, M. A. Karim, “Symbolic-substitution-based operations using holograms: multiplication and histogram equalization,” Opt. Eng. 28, 638–642 (1989).

P. S. Guilfoyle, “Systolic acousto-optic binary convolver,” Opt. Eng. 72, 20–25 (1984).

Proc. IEEE (1)

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE. 72, 850–866 (1984).
[CrossRef]

Other (2)

H. M Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985), Chap. 2, p. 21.

M. A. Karim, A. A. S. Awwal, Optical Computing: An Introduction (Wiley, New York, 1992), Chap. 11, p. 292.

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Figures (14)

Fig. 1
Fig. 1

16-bit 1-D butterfly interconnection network.

Fig. 2
Fig. 2

Optical hardware details of the butterfly interconnection network (after Ref. 8).

Fig. 3
Fig. 3

Block diagram of an N × N bit multiplier.

Fig. 4
Fig. 4

Schematic of a 2 × 2 multiplier: (a) and storage, (b) or stage.

Fig. 5
Fig. 5

Butterfly networks for the (a) and stage, (b) or stage

Fig. 6
Fig. 6

Masks for the multiplier and stage.

Fig. 7
Fig. 7

Masks for the multiplier or stage.

Fig. 8
Fig. 8

Block diagram for a D FF.

Fig. 9
Fig. 9

Schematic of a D FF: (a) and stage, (b) or stage.

Fig. 10
Fig. 10

Diagram of an N-bit PIPO shift register.

Fig. 11
Fig. 11

Butterfly network for the and stage of (a) D FF, (b) N-bit PIPO shift register.

Fig. 12
Fig. 12

Butterfly network for the or stage of (a) D FF, (b) N-bit PIPO shift register.

Fig. 13
Fig. 13

Masks for the D FF and stage.

Fig. 14
Fig. 14

Masks for the D FF or stage.

Tables (2)

Tables Icon

Table 1 Truth Table for a 2 × 2 Multiplier

Tables Icon

Table 2 Truth Table for D FF

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

C 0 = A ¯ 1 A 0 B ¯ 1 B 0 + A ¯ 1 A 0 B 1 B 0 + A 1 A 0 B ¯ 1 B 0 + A 1 A 0 B 1 B 0 ,
C 1 = A ¯ 1 A 0 B 1 B ¯ 0 + A 1 A ¯ 0 B ¯ 1 B 0 + A 1 A ¯ 0 B 1 B 0 + A ¯ 1 A 0 B 1 B 0 + A 1 A 0 B ¯ 1 B 0 + A 1 A 0 B 1 B ¯ 0 ,
C 2 = A 1 A ¯ 0 B 1 B ¯ 0 + A 1 A ¯ 0 B 1 B 0 + A 1 A 0 B 1 B ¯ 0 ,
C 3 = A 1 A 0 B 1 B 0 .
Q ( t + Δ t ) = D ( t ) Q ¯ ( t ) + D ( t ) Q ( t ) .

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