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## Boolean Algebra and Logic Gates

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**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**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**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