Transcript 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
Invented by George Boole, later translated
into diagrams by John Venn, improvised
by Charles Dodgson
George
Self taught professor
from England
Worked on finite
differences in
differential equations
Primarily known for
pioneering works in
modern symbolic
logic.
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
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”
Basic AND and OR
2
1
Models
3
Ferraris
- 1 – Simply Models
- 2 – ONLY pages containing both:
(Models) AND (Ferraris)
- 3 – Simply Ferraris
- 4 – Either Models or Ferraris:
(Models) OR (Ferraris)
4
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)
Some examples
Transistor: can be
used as AND, OR,
XOR (PNP,
NPN…also different
arrangements)
Diodes: serve as NOT
gates
…and
Microchip: a combination of millions of
transistors
John Vann Schematic
Radar
Information copied from:
http://www.biography.com
http://imagesearch.altavista.com
White, R., How Computers Work
http://www.encyclopedia.com