Complete Boolean Algebra for Memristive and Spintronic Asymmetric Basis Logic Functions

TL;DR

This paper develops a complete Boolean algebra framework for asymmetric logic functions used in memristive and spintronic devices, enabling optimized logic circuit design beyond traditional methods.

Contribution

It introduces a novel algebraic framework with identities and theorems tailored for asymmetric logic, improving synthesis and minimization of memristive and spintronic logic circuits.

Findings

28% reduction in computational steps for memristive full adder

Establishes logical relationship between implication and IAND

Provides foundational algebraic tools for future logic optimization

Abstract

The increasing advancement of emerging device technologies that provide alternative basis logic sets necessitates the exploration of innovative logic design automation methodologies. Specifically, emerging computing architectures based on the memristor and the bilayer avalanche spin-diode offer non-commutative or `asymmetric' operations, namely the inverted-input AND (IAND) and implication as basis logic gates. Existing logic design techniques inadequately leverage the unique characteristics of asymmetric logic functions resulting in insufficiently optimized logic circuits. This paper presents a complete Boolean algebraic framework specifically tailored to asymmetric logic functions, introducing fundamental identities, theorems and canonical normal forms that lay the groundwork for efficient synthesis and minimization of such logic circuits without relying on conventional Boolean algebra. Further, this paper establishes a logical relationship between implication and IAND operations. A previously proposed modified Karnaugh map method based on a subset of the presented algebraic principles demonstrated a 28% reduction in computational steps for an algorithmically designed memristive full adder; the presently-proposed algebraic framework lays the foundation for much greater future improvements.