Binary systems

'Binary' means 'two-valued'. Two values occur in logic as TRUE and FALSE, in electronic communication and switching theory as ON and OFF, in graphics as BLACK and WHITE. For those and other interpretations it holds a common theory, going back to the English mathematician George Boole (1815–1864). His theory and its present applications are treated in this book. The 1st chapter contains an introduction into the mathematical foundations and Boolean algebras. The 2nd chapter concerns binary models for circuits and networks, sets and graphs, dynamic systems, logic and diagnostic. Connecting them closely is important for students and shows many new paths to the specialist as well. The 3rd chapter contains algorithms and numerical methods for analytical and computer based calculations. Finally, the author assembles his methodological experience as a university professor. This book is intended for mathematicians, computer scientists, electronics and control engineers, logicians and physicists who are facing Boolean problems. It contains classical methods as well as more recent theories and results obtained by the author. He devoted many years to academic teaching and research on the subjects of this book. Here, he summarizes his experience for new generations of students and university teachers.