Polarization-encoded Optical Shadow-casting Research Articles

Unified negabinary symbolic arithmetic for addition and subtraction with polarization-encoded optical shadow casting

Conventional algorithms process addition and subtraction in different ways. In this paper, by introducing bipolar carries, a unified negabinary symbolic arithmetic for the two operations can be derived, using only the same six substitution rules. Based on the polarization-encoded optical shadow-casting technique, the encoding and decoding patterns for half-addition, half-subtraction and unified arithmetic are designed, with the fixed LED pattern and separate and simultaneous generation of the multi-outputs. The architecture is simple, programmable, cost-efficient, and the addition and subtraction of multiple pairs of bipolar numbers can be handled in parallel in the same manner.

Efficient implementation of arithmetic units based on polarization-encoded optical shadow casting

Carry-free addition and borrow-free subtraction on the redundant modified signed-digit number are adopted for lensless polarizationencoded optical shadow casting (POSC). First, a new recoding truth table, which has a symmetrical complemented relationship between the input minterms (entries that produce an output of 1 or 21) and their corresponding output bits, is developed for the redundant signed-digit numbers. Then, the carry-free POSC adder/subtracter is designed by determining the encoding of the redundant input bits for generating the sum/difference output bits and the source light-emitting-diode pattern. Two design methods are presented: direct implementation and truthtable partitioning. It is shown that the number of pixel subcells in the input encoding of the POSC system can be significantly reduced using the new symmetrical recoding algorithm for the modified signed-digit number representation.

Two-dimensional register design using polarization-encoded optical shadow-casting

An architecture of two-dimensional optical registers employing optical flip-flops is proposed using the polarization-encoded optical shadow casting technique. Two separate designs of the register containing n 2 flip-flops are identified and discussed. A generalized algorithm for sequential logic design is also presented.

Multiple-valued logic based multiprocessor using polarization-encoded optical shadow-casting

An efficient technique for the design of a multiple-valued logic based multiprocessor using polarization-encoded optical shadow-casting is presented. As an illustration, this technique is used to design a multiprocessor which can perform trinary full addition and full subtraction both in parallel.

Multiple-valued logic unit design using polarization-encoded optical shadow-casting

An efficient technique for the design of multiple-valued logic circuits using polarization-encoded optical shadow-casting is presented. As an illustration, a trinary full subtracter is designed using this technique. The resulting logic unit is compared with those obtained by using other algorithms.

Efficient combinational logic circuit design using polarization-encoded optical shadow-casting

An efficient technique for the design of multi-output optical combinational logic circuit using polarization-encoded optical shadow-casting is presented. An 8-to-3 line encoder designed using this technique is compared with that obtained using alternative algorithm.

Polarization-encoded optical shadow casting: Arithmetic logic unit (ALU) design using truth-table partitioning

A memory-efficient arithmetic logic unit (ALU) consisting only of two cells has been designed using a polarization-encoded optical shadow truth table partitioning scheme. The design algorithm for identifying the source patterns, input encoding, and output decoder with possible parallel implementation are also presented.

Morphological transformations based on optical symbolic substitution and polarization-encoded optical shadow-casting systems

By conbining two powerful optical computing techniques, namely, optical symbolic substitution (OSS) and polarization-encoded optical shadow-casting (POSC), morphological or shape transformation operations are demonstrated. Accordingly, erosion, dilation, opening, and closing operations are realized using both OSS and POSC schemes. These morphological operations are used for noise removal in binary images.

Implementation of trinary logic in a polarization encoded optical shadow-casting scheme

The design of various multioutput trinary combinational logic units by a polarization encoded optical shadow-casting (POSC) technique is presented. The POSC modified algorithm is employed to design and implement these logic elements in a trinary number system with separate and simultaneous generation of outputs. A detailed solution of the POSC logic equations for a fixed source plane and a fixed decoding mask is given to obtain input pixel coding for a trinary half-adder, full adder, and subtractor.

Polarization-encoded optical shadow casting: design of trinary multipliers

The polarization-encoded optical shadow casting (POSC) scheme is used to design a 2-digit by 2-digit trinary multiplier. Three design algorithms for identifying the appropriate source patterns, input patterns, and output mask for both serial and parallel operations are presented. The inclusion of analyzer pattern reduces the number of pixel subcells for the POSC inputs.

Multiprocessor design using polarization-encoded optical shadow-casting

An efficient algorithm for designing a multiprocessor logic unit using a polarization-encoded optical shadow casting system is presented. Both efficient minterm pairing and associative memory mapping with dual addresses are exploited for the design. For illustration, the algorithm is used to design a parallel adder-subtracter unit.

Median filtering using polarization-encoded optical shadow casting

A very powerful space-variant image processing technique such as median filtering is performed using the polarization-encoded optical shadow casting (POSC) system. The POSC system is used to process two different noisy images. Two different POSC architectures and input encodings are identified and compared.

Polarization-encoded optical shadow-casting: direct implementation of a carry-free adder

Carry-free addition based on the redundant binary number system is adopted for the lensless polarization-encoded optical shadow-casting (POSC) system. A carry-free POSC adder is designed by determining the codings of (1) the redundant input bits for generating the intermediate sum and intermediate carry and (2) the intermediate sum and intermediate carry for generating the carry-free sum.

Associative polarization-encoded optical shadow casting: gray-level image encoding for serial and parallel operations

An efficient algorithm for designing a serial and parallel multioutput logic unit using an associative polarization-encoded optical shadow-casting technique is presented. Devices designed as such have a unique contentaddressable associative memory where each of the memory locations has dual addresses. For illustration, the proposed algorithm has been used to design a serial-output and a parallel-output 2-bit gray adder.

Separate and simultaneous generation of multioutputs in a polarization-encoded optical shadow-casting scheme: design of half- and full adders and subtractors

A design algorithm for separate and simultaneous generation of multioutputs in a polarization-encoded optical shadow-casting (POSC) scheme is presented. The logic unit truth table is converted into POSC logic equations for true and false logic. These are then solved consistently to obtain source plane, input pixel, and the decoding mask characteristics. The algorithm is used to design binary half-adder and half-subtractor and full adder and full subtractor to carry out all operations with a fixed source plane and a fixed decoding mask. The results have been verified experimentally.

Polarization-encoded optical shadow casting: design of a J-K flip-flop

The device architecture and the corresponding codings of the inputs of a polarization-encoded optical shadow-casting J-K flip-flop are presented. Three different flip-flop designs are considered and compared.

Polarization-encoded optical shadow-casting programmable logic array: simultaneous generation of multiple outputs

A scheme for designing a content-addressable memory (CAM) using polarization-encoded optical shadow-casting (POSC) is proposed. Such a programmable logic array requires comparatively less memory storage because of the built-in reduction in the truth table entries. The scheme is implemented by copying the truth table entries directly into the corresponding input pixel subcells. The proposed POSC CAM generates all its outputs simultaneously, thus eliminating the design requirement of switching either LED sources or decoding masks. For illustration, a 4-input 4-output 2x2 binary multiplication unit is designed using this scheme.

Polarization-encoded optical shadow-casting scheme: design of multioutput trinary combinational logic units

The input encoding algorithm of the polarization-encoded optical shadow-casting (POSC) scheme is modified to include the design of trinary combinational logic units. For illustration, the modified algorithm is deterministically employed in the design of trinary adders. Two design approaches are examined for identifying the constraints and flexibilities that are encountered depending on whether the zero-output conditions are considered. The more complicated POSC overlap equations are handled by incorporating LED source encoding to the input encoding process.