Optical arithmetic/logic unit based on residue arithmetic and symbolic substitution

Capps, C. David; Falk, R. Aaron; Houk, Theodore L.

doi:10.1364/ao.27.001682

Cited by 30 publications

(4 citation statements)

References 3 publications

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“…In RB representation, an integer D obtained by D = 'aj2hu/21, a1{O, 1) (2) where [ 1 represents the rounding to the upper integer. In RB representation, an integer D obtained by D = 'aj2hu/21, a1{O, 1) (2) where [ 1 represents the rounding to the upper integer.…”

Section: Redundant Binary Representationmentioning

confidence: 99%

<title>Multiplexed symbolic substitution based on optical correlator for optical parallel addition with redundant binary number</title>

Noh¹,

Kim

et al. 1996

SPIE Proceedings

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A multiplexed symbolic substitution method based on an optical correlator is proposed for an optical parallel addition with redundant binary number. The minimum average correlation energy (MACE) filter, which has very low sidelobes and sharp correlation peaks, is chosen as the optical correlation filter in the recognition phase of symbolic substitution. The sixteen coded input patterns of the redundant binary numbers are classified six groups according to the addition results to minimize the number of recognition filters. To implement the smaller optical system, six recognition/substitution filters are multiplexed in two filter planes with spatial carrier frequencies. Through the computer simulation, it is confirmed that the proposed multiplexed symbolic substitution method is suitable for implementation of the optical parallel adder.

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Section: Redundant Binary Representationmentioning

confidence: 99%

<title>Multiplexed symbolic substitution based on optical correlator for optical parallel addition with redundant binary number</title>

Noh¹,

Kim

et al. 1996

SPIE Proceedings

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“…A number of different ways [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] of eliminating or advancing carries have been proposed. Nonbinary encoding such as the residue number system 5,6 and the modified signed-digit ͑MSD͒ number system [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] are of significant interest since they can eliminate or limit the carry propagation.…”

Section: Introductionmentioning

confidence: 99%

Programmable modified-signed-digit addition module based on binary logic gates

Zhang

Karim

1999

Opt. Eng

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A new binary logic based modified-signed-digit (MSD) adder is proposed. By encoding MSD digits in pairs of binary bits, each of the four MSD transforms can be represented by two cascaded binary logic operations. This leads to the design of a compact and integrated programmable MSD addition module. The three operation steps in the MSD addition can be realized using this same module simply by programming the decoding masks.

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“…Techniques to improve the accuracy include the use of residue number system [1,2] the redundant analogue technique [3] and so-called 'digital multiplication by analogue convolution' (DMAC) techniques [4-1 1].…”

mentioning

confidence: 99%

<title>Improved optical matrix-vector multiplier</title>

1999

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An improved optical matrix-vector multiplication is performed by convolution process. The multiplicand binary numbers are represented by on/off states of light sources and the multiplier binary numbers are recorded on a spatial light modulator. Cylindrical optics is used as free space interconnection. The convolution coefficients are recorded on a CCD array. The output of the CCD array are added in a computer to yield the result of multiplication. The operation is completely digital and needs no analog to digital conversion. Because of parallel operation in two dimensions, the processing speed is greatly increased. INTRODUCTIONThe desire for faster computation has placed demand of higher speed and computing power on silicon IC based computing machines. As an alternative to the silicon based technology, some of the unique features of optics, such as parallelism of data paths, non-interacting communication between parallel channels and representation of data in two or three dimensions, are being utilized in meeting the demands of high speed computing.

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Optical arithmetic/logic unit based on residue arithmetic and symbolic substitution

Cited by 30 publications

References 3 publications

<title>Multiplexed symbolic substitution based on optical correlator for optical parallel addition with redundant binary number</title>

<title>Multiplexed symbolic substitution based on optical correlator for optical parallel addition with redundant binary number</title>

Programmable modified-signed-digit addition module based on binary logic gates

<title>Improved optical matrix-vector multiplier</title>

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