Boolean Algebra and Logic Gates CE 40 B 18 June 2003

Basic Definitions  Common Postulates Closure Associative Law Commutative Law Identity Element Inverse Distributive Law  Field set of elements with two binary operators

Axiomatic Definition of Boolean Algebra  George Boole  Two binary operators (+ and ·)  Huntington Postulates Closure, Identity, Commutative, Distributive, Complement  Show that Huntington Postulates are valid for B = {0,1}

Basic Theorems and Properties of Boolean Algebra  Duality Expression remains valid even after operators and identity elements are interchanged  Some theorems x + xy = x (x + y)’ = x’y’

Boolean Functions  Logical relationship between binary variables  Can be represented by a truth table  Can be transformed into a logic diagram  Example: f = x + y’z

Example – f = x + y’z

Canonical and Standard Forms  Maxterms and Minterms  Canonical Forms Sum of Minterms Product of Maxterms  Standard Forms Sum of products Product of sums

Other Logic Operations  Formed from combination AND, OR, and NOT.  16 possible functions for 2 binary variables

Digital Logic Gates

Integrated Circuits  IC Silicon chip containing electronic components for constructing digital gates  Different Levels of Integration Circuit complexity Number of logic gates in one package SSI, MSI, LSI, VLSI

Integrated Circuits  Digital Logic Families Circuit technology – how the logic gates are constructed TTL, ECL, MOS, CMOS Characteristics  Fan-out  Fan-in  Power dissipation  Propagation delay  Noise margin

Integrated Circuits  Computer-Aided Design Complex designs require computers Electronic Design Automation (EDA) Hardware Description Language (HDL)  Verilog, VHDL