Boolean Algebra and Logic Gates

CE 40 B18 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