Combinational Logic

Abstract

To express any body of ideas in a meaningful form, some sort of logical framework is required. This book is concerned with digital systems, and the framework used is that based on a mathematical logic developed largely by the English mathematician George Boole. Boole published the basic axioms and rules for a two-valued algebra in 1854, but for the rest of the nineteenth century his work remained firmly in the province of mathematics (see Boole, 1953). Huntington (1904) published a set of postulates for a two-state algebra which forms the basis of our modern approach to boolean algebra. However, it was not until 1938 that this algebra was shown to be a useful tool for the engineer. Shannon (1938) introduced a switching algebra, adapting boolean algebra for use in the analysis of relay switching networks used in telephone systems. The development of digital systems since the 1940s, initially restricted to the digital computer, now extends over a seemingly unlimited range of applications. A grasp of the structure of Boole’s two-state logic is essential to the understanding of switching theory, which is itself fundamental to the design of all digital systems.