A novel generic modulo‐2 graph with full set taxonomical conversion to parallel prefix adders. (3rd January 2022)

• Record Type: Journal Article
• Authors: Rahimi, M.; Ghaznavi‐Ghoushchi, M. B.
• Is Part Of: International journal of circuit theory and applications. Volume 50:Number 4(2022)
• Page Start: 1143
• Page End: 1159
• Publication Date: 2022-01-03
• Subjects: conversion algorithm -- generic graph -- parallel prefix adders -- trilinear coordinates; Electric circuit analysis -- Periodicals; 621.319205
• DOI: 10.1002/cta.3148
• Languages: English
• ISSNs: 0098-9886

Abstract

Abstract: This paper proposes a novel generic modulo‐2 graph that can be converted to parallel prefix adders (PPA). Also, a conversion algorithm for converting the proposed graph to PPAs is proposed in this paper. The conversation algorithm can be applied on N‐bit Generic modulo‐2 graph, and this graph is converted to N‐bit PPAs. When the proposed conversion algorithm is applied to generic modulo‐2 graph, this graph is converted to Brent‐Kung, Sklansky, Kogge‐Stone, Harris, Ladner‐Fischer, Han‐Carlson, and Knowles adders. Moreover, PPAs are shown in trilinear coordinates to represent the final PPAs, which generic graph converted to them. Furthermore, the add operation is done by generic graph and also the correctness of add function of this graph is investigated by "Boolean decision diagram." Abstract : Applying conversion algorithm on the proposed 8‐bit generic adder graph (bottom plate) to achieve an 8‐bit Kogge‐Stone (0, 0, 2) adder (top plate). There are three steps (shown in three inner layers) for converting the 8‐bit generic graph to Kogge‐Stone (0, 0, 2). The parameters of algorithm for converting from the generic graph to Kogge‐Stone (0, 0, 2) adder are: "Starting Row to Simplify (R0)", "Period (T)", "Simplified Rows in each Period (SR)", "Simplified Cells per Row (SC)", "Number of Returns of each row (E)" and "Gray Cells (G)".