boolean algebra and logic gates

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Boolean algebra and logic gates

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Presentation on Boolean Algebra and Logic Gates

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  • Boolean algebra and logic

    gates

  • George Boole

    mathematician and logician

    formalized logic in a mathematical manner

    father of Boolean algebra and modern symbolic logic

  • George Boole

  • Boolean algebra

    or Boolean logic

    The Mathematical Analysis of Logic 1847.

    defines relations between prepositions

    mathematical calculus of truth values

  • C. E. Shannon

    Boolean operators can be used in logic gates

    Claude E. Shannon 1938.

    a century after Boolean logic

    revolution in informatics

  • Boolean algebra and logic gates

    logic gates control the flow of electric current through integrated circuits

    they control it based on Boolean algebra

    True or 1 presence of electric tension

    False or 0 absence of electric tension

  • Logic gates

    atomic prepositions

    +

    logic operators

    =

    logic gates

  • Logic gates

    Logic gate AND

    A B AB

    0 0 0

    0 1 0

    1 0 0

    1 1 1

  • Logic gates

    Logic gate OR

    A B A+B

    0 0 0

    0 1 1

    1 0 1

    1 1 1

  • Logic gates

    Logic gate NOT

    A ~A

    0 1

    1 0

  • Logic gates

    Logic gate NAND

    A B ~(AB)

    0 0 1

    0 1 1

    1 0 1

    1 1 0

  • Logic gates

    Logic gate NOR

    A B ~(A+B)

    0 0 0

    0 1 1

    1 0 1

    1 1 1

  • Logic gates

    other gates

    XNAND

    XNOR

    MINTERM

    MAXTERM

  • Logic gates

    goal simplifying complex operations

    why? faster, cheaper, smaller

    how? researching and studying rules

    no algorithms or shortcuts

  • Moores law

    "The number of transistors incorporated in a chip will approximately double every 24

    months."

    computers

    faster, smaller and better overall performance

  • Recapitulation

    George Boole

    Boolean algebra and modern symbolic logic

    C. E. Shannon

    Boolean algebra and integrated circuits

    no modern computers without Boolean algebra

  • Questions

    1. Name a logic operator and say when its

    output value equals 0!

    2. Who discovered that Boolean algebra

    can be used for managing the flow of

    electric current in integrated circuits?

    3. What does Moores law say?

  • Any

    questions?