RULES OF BOOLEAN ALGEBRA

Here is the list of Boolean rules that can help in simplifying the Boolean expressions quickly and easily as well, if you memorize them all.

IDENPOTENCY RULE:

X+0=x (enable) X+1=1 (disable)
X+x=x
x.1=x (enable) x.0=0 (disable)
x.x=x

 

COMMUTATIVE PROPERTY:

X+y=y+x
x.y=y.x

 

ASSOCIATIVE PROPERTY:

(x+y)+z=x+(y+z)
(x.y).z=x.(y.z)

 

DISTRIBUTED PROPERTY:

x.(y+z)=(x.y)+(x.z)
X+(y.z)=(x+y).(x+z)

 

DE-MORGAN’S THEOREM:

(x+y)’ = x’ . y’
(x.y)’ = x’ + y’
                 Or
(a.b + cd)’ = (a.b)’ . (cd)’
                   = (a’ + b’) . (c’ + d’)

 

ABSORPTION THEOREM:

(x+x’z) = (x+x’) (x+z)
             = (1) (x+z)
             = (x+z)
                         Or
X+x’abc
Let abc = y
X+x’y = (x+x’) (x+y)
           = 1(x+y)
           = (x+y)
                         Or
           = (x+abc)

 

FUNCTIONS:

 OR (x+y)
Logic sum
 AND (x.y)
Product
 NOT x’ y’
Complement

 

EXISTANCE OF 2 VARIABLES:

X = 1      if      x is not equal to zero
‎ X = 0     if      x is not equal to one‎

 

COMPLEMENTRY PROPERTY:

 A + A’ = 1
 A . A’ = 0

 

 

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