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 Algebra de Boole es una herramienta para expresar y analizar
las operaciones de los circuitos lógicos.
◦ Variable.- es un símbolo que representa una magnitud lógica
◦ Complemento.- es el inversode la variable
◦ Literal.- es una variable o su complemento
 TEOREMA= REGLA
 El teorema de Boole nos sirve para simplificar las expresiones
y los circuitos lógicos.
 Con la simplificación delos circuitos nos permite solo utilizar
el número optimo de circuitos integrados en una tarjeta
electrónica o en cualquier aplicación.
The commutative laws are applied to addition andmultiplication. For addition, the commutative law states
In terms of the result, the order in which
variables are ORed makes no difference.
A + B = B + A
In terms of the result, the order in which
variablesare ANDed makes no difference
For multiplication, the commutative law states
difference.
AB = BA
The associative laws are also applied to addition and
multiplication. For addition, theassociative law states
When ORing more than two variables, the result is
the same regardless of the grouping of the variables.
A + (B +C) = (A + B) + C
For multiplication, the associative law states
WhenANDing more than two variables, the result is
the same regardless of the grouping
The distributive law is the factoring law. A common
variable can be factored from an expression just as in
ordinaryalgebra. That is
AB + AC = A(B+ C)
The distributive law can be illustrated with equivalent
circuits:
B + C
C
B
B AB
X
A
A X
C
A
AC
A(B+ C) AB + AC
Rules of Boolean algebra can beillustrated with Venn
diagrams. The variable A is shown as an area.
The rule A + AB = A can be illustrated easily with a diagram. Add
an overlapping area to represent the variable B.
The overlap regionbetween A and B represents AB
A AB.
B
AB =
The diagram visually shows that A +
 Todas las expresiones booleanas constan
de combinaciones de las operaciones
básicas OR, AND, NOT.
...
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