Optical EngineeringEfficient optical negabinary modified signed-digit arithmetic: one-step addition and subtraction algorithms
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Efficient one-step addition and subtraction algorithms are proposed. The arithmetic operations use the negabinary modified signed-digit number representation, which is an extension of the negabinary number system. Truth tables representing the required symbolic substitution computation rules are determined. Then a reduction of the number of the symbolic substitution computation rules is achieved by considering the digits in the lower positions of the negabinary modified signed digits in the computation. The proposed algorithms are very suitable for optical holographic and nonholographic implementations. An incoherent correlation based on the efficient shared content-addressable memory (SCAM) is suggested as an optoelectronics implementation.