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Oct 2007 E1.2 Digital Electronics I 3.1 Lecture 3: Basic Log ic Gates & Bool ean Expressions Professor Peter Cheung Department of EEE, Imperial College London (Floyd 3.1-3.5, 4.1) (Tocci 3.1-3.9) Oct 2007 E1.2 Digital Electronics I Points Ad dressed in this Lecture • What are the basic l ogi c gates? • What i s Bool ean al gebra? • Boolean vari abl es & expressions • Boolean algebr a as a way to wr ite down l ogi c • Bool ean Operators • Truth tables • Rel ati onships between logic gat es & Boolean expressions Oct 2007 E1.2 Digital Electronics I Boolean Algebra • Digital electronic systems manipulate binary information • To design such systems we need a convenient mathematical framework  – useful systems are often too complicated to keep in our head  – Boolean algebra provides this framework • Points in a circuit are repres ented by Bool ean Variabl es • Bool ean algebr a all ows us to speci fy rel ationships between Boolean variables  – Hence Boolean algebra can be used as a design tool for digital electronic circuits Oct 2007 E1.2 Digital Electronics I Boolean Variables • Boolean variabl es take the value either 0 or 1 only  – if a variable doesn't have the value 0, then it must hav e the value 1  – if a variable doesn't have the value 1, then it must hav e the value 0 • In di gi tal electr onics:  – Boolean 0 and 1 correspond to the binary 0 and 1 • In logic:  – 1 and 0 are sometimes called true and false • We use symbols to r epr esent Boolean vari ables  – just like with ordinary algebra  – eg: A, B, C, X, Y, Z, etc  – typically a single character  – typically upper case • Thr ee Logic oper ations: AND, OR, NOT

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