Boolean vector algebraic structures: properties and applications to digital logic simulation

Abstract

Boolean algebra is the basic mathematic used in the analysis and synthesis of binary systems. Technological advances have led to an increasing interest in multivalued logic systems where more than two logical values are used. In the application of multivalued logic, each logical value could often be represented by a Boolean vector, ie a vector with binary components (0 or 1). Therefore, it is quite important to have a thorough understanding of properties embedded in the algebraic structures using Boolean vectors as basic operands. This gives the motivation for this study. Boolean vector operations are introduced and two major modes associated with the complement are characterized. Then we define a Boolean vector E-algebra and its major features are given. Finally, some applications are discussed and illustrated.