4

Boolean algebra

4.1 Introduction

Boolean algebra can be thought of as the study of the set {0, 1} with the operations + (or),. (and), and (not). It is particularly important because of its use in design of logic circuits. Usually, a high voltage represents TRUE (or 1), and a low voltage represents FALSE (or 0). The operation of OR (+) is then performed on two voltage inputs, using an OR gate, AND(.) using an AND gate and NOT is performed using a NOT gate. This very simple algebra is very powerful as it forms the basis of computer hardware.

You will probably have noticed that the operations of Λ (AND), ∨ (OR), and ¬ (NOT) used in Chapter 3 for propositions are very similar to the operations ∩ (AND), ∪ OR, and ′ (NOT) (complement) used for sets. ...

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