25 November 2008

Boolean Algebra

Basic identities used in boolean algebra digital logic.

Note that X' means not X, the complement of X
  1. X+0 = X
  2. X.1 = X
  3. X+1= 1
  4. X.0 = X
  5. X+X = X
  6. X.X=X
  7. X+X'=1
  8. X.X'=0
  9. X''=X

Other boolean algebra properties.

  • Commutative: X+Y = Y+X
  • Associative: X+(Y+Z) = (X+Y)+Z
  • Distributive: X(Y+Z) = XY + XZ
  • DeMorgan's: (X+Y)' = X'+Y'
The identities below are useful for simpling the logic equations.

  • X(X+Y)=X
  • (X+Y)(X+Y')=X
  • X(X'+Y)=XY
Boolean algebra digital logic tutorial.

2 comments:

Anonymous said...

your DeMorgans theory is wrong

(X+Y)' = X'+Y'

should be

(X+Y)' = X'.Y'

What is an Independent Variable said...

Very knowledgeable and informative blog.Boolean algebra is one of the most interesting and important algebraic structure which has significant applications in switching circuits, logic and many branches of computer science and engineering.