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Boolean Algebra: (Wikipedia Definition)

In mathematics and mathematical logic, Boolean algebra is the subarea of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 (respectively). Instead of elementary algebra where the values of the variables are numbers, and the main operations are addition and multiplication, the main operations of Boolean algebra are the conjunction and, denoted ∧, the disjunction or, denoted ∨, and the negation not, denoted ¬.

Boolean algebra was introduced in 1854 by George Boole in his book An Investigation of the Laws of Thought. According to Huntington the term "Boolean algebra" was first suggested by Sheffer in 1913.

Boolean algebra has been fundamental in the development of computer science and is yet the basis of the abstract description of digital circuits. It is also used in digital logic, computer programming, set theory, and statistics.

 

Basic operations

The basic operations of Boolean algebra are the following ones:

  • And (conjunction), denoted x∧y (sometimes x AND y or Kxy), satisfies x∧y = 1 if x = y = 1 and x∧y = 0 otherwise.
  • Or (disjunction), denoted x∨y (sometimes x OR y or Axy), satisfies x∨y = 0 if x = y = 0 and x∨y = 1 otherwise.
  • Not (negation), denoted ¬x (sometimes NOT x, Nx or !x), satisfies ¬x = 0 if x = 1 and ¬x = 1 if x = 0.

If the truth values 0 and 1 are interpreted as integers, these operation may be expressed with the ordinary operations of the arithmetic:

x∧y = xy,
x∨y = x + y - xy,
¬x = 1 - x.
 
 

 dgital Logic:  

 

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=DIG1302

 

http://www.neuroproductions.be/logic-lab/   

 

 

Monday 2/10

 

 

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=DIG1202

 

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=DIG2503

 

Gates

 

Useful Links:

 Logic gate online simulator: http://www.course.com/downloads/computerscience/aeonline/7/1/index.html

 

 Boolean Algebra tutorial: http://www.doc.ic.ac.uk/~dfg/hardware/HardwareLecture02.pdf

 

http://www.facstaff.bucknell.edu/mastascu/elessonshtml/logic/logic1.html