This chapter introduces the essential information required for the rest of the book. This includes a description of Boolean algebra, the mathematical language of digital electronics, and the logic gates used to implement Boolean functions. Also covered are the ‘tools' of digital electronics such as truth tables, timing diagrams and circuit diagrams. Finally, certain concepts such as duality, positive and negative assertion level logic and universal gates, that will be used in later chapters, are introduced.
1. Boolean algebra - an Introduction
The algebra of a number system basically describes how to perform arithmetic using the operators of the system acting upon the system's variables which can take any of the allowed values within that system. Boolean algebra describes the arithmetic of a two-state system and is therefore the mathematical language of digital electronics. The variables in Boolean algebra are represented as symbols (e.g. A, B, C, X, Y etc.) which indicate the state (e.g. voltage in a circuit). In this book this state will be either 0 or 1.' Boolean algebra has only three operators: NOT, AND and OR. The symbols representing these operations, their usage and how they are used verbally are all shown in Table 1.1. Note that whereas the AND2 and OR operators operate on two or more variables the NOT operator works on a single variable.
In other textbooks, and occasionally later on in this one, you may see these states referred to as HIGH and LOW or ON and OFF.
•Sometimes the AND symbol, A.B is omitted and the variables to be ANDM are just placed together as AB. This notation will be adopted in later chapters.