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Boolean Algebra

Boolean Algebra. By Lindsey Curtis & Tomas Filip. Boolean Algebra. An abstract mathematical system used to describe relationships between sets Mainly used in computer science to manipulate logical statements

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Boolean Algebra

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  1. Boolean Algebra By Lindsey Curtis & Tomas Filip

  2. Boolean Algebra • An abstract mathematical system used to describe relationships between sets • Mainly used in computer science to manipulate logical statements • Invented by George Boole, later translated into diagrams by John Venn, improvised by Charles Dodgson

  3. George • Self taught professor from England • Worked on finite differences in differential equations • Primarily known for pioneering works in modern symbolic logic.

  4. Practical Applications • Internet search engines • Study of information theory, probability • Expression of electrical networks in Boolean notation has aided the development of switching theory and the design of computers

  5. Under the Hood • Boolean logic uses various switches to show the relationship between groups, indicating what is in each set alone, what is jointly contained in both, and what is contained in neither.These are: AND, OR, XOR, NOT, BUT, INV, NAND, NOR, and XOR • For every SWITCH there is a specific “Truth Table”

  6. Basic AND and OR 2 1 3 4 BOTH Models Ferraris • - 1 – Simply Models • - 2 – ONLY pages containing both: (Models) AND (Ferraris) • - 3 – Simply Ferraris • - 4 – Either Models or Ferraris: (Models) OR (Ferraris)

  7. Equally Important • Boolean algebra is closely tied to the concepts of binary #’s (0’s or 1’s), representing either flow or no flow of electric current…or more-less “on” vs. “off” • In electronics, devices are assembled from different types of circuits, which are made with these logic gates (in form of electrical components) • Among many other things, logic gates can perform calculations with binary numbers (full / half adders)

  8. Some examples • Transistor: can be used as AND, OR, XOR (PNP, NPN…also different arrangements) • Diodes: serve as NOT gates

  9. …and Microchip: a combination of millions of transistors

  10. John Vann Schematic Radar

  11. Information copied from: • http://www.biography.com • http://imagesearch.altavista.com • White, R., How Computers Work • http://www.encyclopedia.com

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