Boolean Alebra & Functions

Boolean Algebra & Functions

Basic rules of Boolean Algebra:

The basic rules for simplifying and combining logic gates are called Boolean algebra in honour of George Boole (1815 – 1864).

x · y  =  y · x

x + y  =  y + x

x · (y · z)  =  (x · y) · z

x + (y + z)  =  (x + y) + z

x · (y + z)  =  (x · y) + (x · z)

x + (y · z)  =  (x + y) · (x + z)

x · x  =  x

x + x  =  x

x · (x + y)  =  x

x + (x · y)  =  x

x · x’  =  0

x + x’  =  1

(x’)’  =  x

(x · y)’  =  x ‘ +  y’

(x + y)’  =  x’ · y’