Boolean Algebra and Logic Gates

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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) xy

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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 yz

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Example f x yz
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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