Abstract
Contrary to the traditional base 2 binary number system, used in today's computers, in which a complex number is represented by two separate binary entities, one for the real part and one for the imaginary part, Complex Binary Number System (CBNS), a binary number system with base (−1+j), is used to represent a given complex number in single binary string format. In this paper, CBNS is reviewed and arithmetic algorithms for this number system are presented. The design of a CBNS-based parallel processor utilizing content-addressable memory for implementation of associative dataflow concept has been described and software-related issues have also been explained. Keywords—binary number; complex binary; parallel processing; content-addressable; memory; associative dataflow; compiler; operating system I. INTRODUCTION
Highlights
A complex number consists of two components, namely the real part and the imaginary part, and it represents a point in a two-dimensional space
Considering that Complex Binary Number System (CBNS) provides an efficient format for representing data and ASSOCIATIVE DATAFLOW CONCEPT (ADC) exhibits a promising future for parallel processing, it was natural for researchers to consider amalgamating the two ideas into designing of a Complex Binary Associative Dataflow Processor (CBADP) which takes advantage of the best features found in both concepts
CBADP associative memory consists of a comparand register which contains the data to be compared against the contents of the memory array, a mask register used to mask off portions of the data word(s) which do not participate in the operations, a memory array containing a collection of memory cells providing storage and search medium for the data, and a responder indicating success or failure of a search operation
Summary
A complex number consists of two components, namely the real part and the imaginary part, and it represents a point in a two-dimensional space. To obtain CBNS representation of imaginary numbers, we multiply the CBNS representation of corresponding positive number with 11 (equivalent to (+j) base10 ) or 111 (equivalent to (–j) base10 ) according to the multiplication algorithm given in sub-section B. To represent a complex number in CBNS, we add the CBNS representation of real part with the CBNS representation of the imaginary part according to the addition algorithm given in sub-section B. Considering that CBNS provides an efficient format for representing data and ADC exhibits a promising future for parallel processing, it was natural for researchers to consider amalgamating the two ideas into designing of a Complex Binary Associative Dataflow Processor (CBADP) which takes advantage of the best features found in both concepts. Each component of the diagram is described in the following sub-sections
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