NDLI: Extended Boolean algebra for asynchronous quasi-delay-insensitive logic

Content Provider	IET Digital Library
Author	Tran, Linh Duc Pham, Thanh Chi Kavehei, Omid Burton, Peter C. M. Matthews, Glenn I.
Abstract	Asynchronous quasi-delay-insensitive (QDI) circuits have recently become an active research area in digital logic design. In contrast with synchronous paradigms, QDI approaches utilise threshold gates with hysteresis, such as Muller C-element and null convention logic (NCL) gates. However, there are no existing methods to explicitly describe these hysteretic logic gates in Boolean algebra. Therefore, in this study, the authors extend the Boolean algebra with two novel operators, named completion and truth tuple, to enable explicit expressions for all QDI elements such as C-elements, NCL, NCL+, latches and several non-conventional hysteretic threshold gates that they call dual-threshold logic. In addition, they develop a set of 16 laws and theorems for these new operators to create a complete novel algebraic extension for QDI logic. It is demonstrated that the authors' extended algebra is a complete approach for explicit design and analysis of QDI circuits, including logic description, equation formation from truth table, expression simplification and conversion, and even gate mapping and corresponding CMOS implementation. They also provide an analysis and solution for netlist corruption problems during the synthesis process of existing QDI design flows, as well as a complete design example using the extended Boolean algebra with different QDI design styles.
Starting Page	1201
Ending Page	1213
Page Count	13
ISSN	1751858X
Volume Number	14
e-ISSN	17518598
Issue Number	Issue 8, Nov (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cds/14/8
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cds.2020.0062
Journal	IET Circuits, Devices & Systems
Publisher Date	2020-08-17
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Algebraic Extension Asynchronous Circuit Asynchronous Quasi-delay-insensitive Logic Boolean Algebra C-elements CMOS Integrated Circuit Complete EDA Tool Support Delay Digital Circuit Design, Modelling And Testing Digital Logic Design Dual-threshold Logic Explicit Design Expression Simplification Extended Boolean Algebra Formal Logic Gate Mapping Hysteretic Logic Gate Logic And Switching Circuit Logic Circuit Logic Description Logic Design Method Logic Element Logic Gate Mature Industrial EDA Tool Support Muller C-element Named Completion NCL Nonconventional Hysteretic Threshold Gate Null Convention Logic Gate QDI Circuit QDI Design Styles QDI Element QDI Logic Quasidelay-insensitive Circuit Quasidelay-insensitive Logic Synchronous Paradigms Threshold Logic Truth Tuple
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering

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