Negative binary arithmetic algorithms for digital parallel optical computation

Abstract

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.

All-optical polarization-encoded negabinary signed-digit adder designs using terahertz-optical-asymmetric-demultiplexer switches

“…In this regard, another competitive number representation system referred to as negabinary uses a negative base to handle bipolar data (Zohar, 1970;Zhang & Karim, 1998). Negabinary number representation was proposed to implement optical linear algebra processors-OLAP (Perlee & Casasent, 1986), optical complex matrix operation (Li et al, 1994), optical one step adder (Zhang & Karim, 1998), and optical modular multiplication (Li et al, 1999). Due to its redundancy, the NMSD has the potential to be used in implementing fast VLSI multipliers and dividers (Lakshmi & Dhar, 2011;Jaberipur & Parhami, 2008).…”

Parallel optical negabinary arithmetic based on logic operations

“…Unlike the MSD and binary number systems, negabinary 22 can uniquely represent both positive and negative numbers without sign bits. In this paper, we present parallel optical negabinary arithmetic operations.…”

Modified engagement method for matrix operation

“…In optics, more freedom with interconnections is possible. A variety of schemes have been reported for matrix operation, of which we list only a few: coherent, 2 incoherent, 3 binary encoded, 4 negative binary encoded, 5 outer product, 6 and the systolic method. 7 Different optical matrix operation systems have different performances and requirements.…”

“…Generally speaking, analog optical matrix multipliers have a limited accuracy 18-10 bits2. 2,8 Digital-encoding techniques, 4,5 which equivalently augment the processor size to increase accuracy, inflate the preprocessing and postprocessing costs 9 that are required to implement a matrix operation. However, the systolic and@or engagement array, which have been successfully implemented by VLSI technology, is worth studying, both from an optical view point 7,10 and an electronic view point.…”

“…5 The local memory of the PE can be realized when ''the charges of the photodetector are accumulated'' as suggested by Bocker et al 10 The two-dimensional ring interconnections between PE's can be realized in optics in the following methods: the Wang et al one-dimensional ring interconnection topology 24 can be extended to the two-dimensional crossed-ring case. Brenner and Lohmann 25 and Jahn and Dä schner 26 have suggested and demonstrated several implementation methods that incorporate optical ring interconnection networks, but they do not use the name ring; they refer to it as cyclic shifting.…”