Arithmetic operations in optical computations using a modified trinary number system

Signed-negabinary-arithmetic-based optical computing by use of a single liquid-crystal-display panel

Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique. For addition and subtraction, one of the operands in decimal form is converted into the unsigned negabinary form, whereas the other decimal number is represented in the signed negabinary form. The result of operation is obtained in the mixed negabinary form and is converted back into decimal. Matrix-vector multiplication for unsigned negabinary numbers is achieved through the convolution technique. Both of the operands for logical operation are converted to their signed negabinary forms. All operations are implemented by use of a unique optical architecture. The use of a single liquid-crystal-display panel to spatially encode the input data, operational kernels, and decoding masks have simplified the architecture as well as reduced the cost and complexity.

Parallel optical negabinary arithmetic based on logic operations

On the basis of signed-digit negabinary representation, parallel two-step addition and one-step subtraction can be performed for arbitrary-length negabinary operands. The arithmetic is realized by signed logic operations and optically implemented by spatial encoding and decoding techniques. The proposed algorithm and optical system are simple, reliable, and practicable, and they have the property of parallel processing of two-dimensional data. This leads to an efficient design for the optical arithmetic and logic unit.

Negative binary arithmetic algorithms for digital parallel optical computation

Based on a negative binary number system, an algorithm with weighted-shifted addition, parallel-array multiplication, and a two-stage-array complex operation is proposed to carry out the multiplication of two complex numbers. The complex multiplication is performed without signs, carries, and recoding. The algorithm is suitable for optical implementation, and an optical parallel architecture is suggested. The experimental result is also given.

Modified signed-digit optical processors using computer-generated holograms

Modified signed-digit (MSD) numbers offer convenient parallel addition and subtraction of bits. The parallel addition of any two MSD numbers, no matter what the values of their bits may be, requires only three bit-pattern transformations. To perform such transformations optically, however, MSD data must be represented in a form suitable for cascade connection. Proposed here is a new cascade-connective MSD optical processor. Adding principles are successfully demonstrated by using an optical threshold device array in addition to new computer-generated holograms that are adjusted to equalize the intensity of their diffracted light beams.