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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

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Boolean Algebra and Logic Gates

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Boolean algebra and logic gates l.jpg

Boolean Algebra and Logic Gates

CE 40 B

18 June 2003


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Basic Definitions

  • Common Postulates

    • Closure

    • Associative Law

    • Commutative Law

    • Identity Element

    • Inverse

    • Distributive Law

  • Field

    • set of elements with two binary operators


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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}


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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’


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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


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Example – f = x + y’z


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Canonical and Standard Forms

  • Maxterms and Minterms

  • Canonical Forms

    • Sum of Minterms

    • Product of Maxterms

  • Standard Forms

    • Sum of products

    • Product of sums


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Other Logic Operations

  • Formed from combination AND, OR, and NOT.

  • 16 possible functions for 2 binary variables


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Digital Logic Gates


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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


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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


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Integrated Circuits

  • Computer-Aided Design

    • Complex designs require computers

    • Electronic Design Automation (EDA)

    • Hardware Description Language (HDL)

      • Verilog, VHDL


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