Logic Functions And Equations

The expanded and updated 2nd edition of this classic text offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science. The approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods.

Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications.

The field of binary Logics has two main areas of application, the Digital Design of Circuits (related to Electrical Engineering) and Propositional Logics (related to Mathematics, Artificial Intelligence, Complexity etc.). In both cases it is quite possible to teach the theoretical foundations and to do some exercises, but in both cases the examples that can be done in class and by hand are far away from examples that are relevant for practical problems.

The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean Algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits.