Basic Postulates in Boolean Algebra
#Identity Law – A term OR´ed with a “0” or AND´ed with a “1” will always equal that term
A + 0 = A A variable OR’ed with 0 is always equal to the variable
A . 1 = A A variable AND’ed with 1 is always equal to the variable
#Idempotent Law – An input that is AND´ed or OR´ed with itself is equal to that input
A + A = A A variable OR’ed with itself is always equal to the variable
A . A = A A variable AND’ed with itself is always equal to the variable
#Complement Law – A term AND´ed with its complement equals “0” and a term OR´ed with its complement equals “1”
A . A' = 0 A variable AND’ed with its complement is always equal to 0
A + A' = 1 A variable OR’ed with its complement is always equal to 1
#Commutative Law – The order of application of two separate terms is not important
A . B = B . A The order in which two variables are AND’ed makes no difference
A + B = B + A The order in which two variables are OR’ed makes no difference
#Double Negation Law – A term that is inverted twice is equal to the original term
(A')' = A A double complement of a variable is always equal to the variable
#DeMorgan´s Theorem – There are two “de Morgan´s” rules or theorems,
(1) Two separate terms NOR´ed together is the same as the two terms inverted (Complement) and AND´ed for example: (A+B)' = A' . B'
(2) Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and OR´ed for example: (A.B)' = A' + B'
Other algebraic Laws of Boolean not detailed above include:
#Distributive Law – This law permits the multiplying or factoring out of an expression.
A(B + C) = A.B + A.C (OR Distributive Law)
A + (B.C) = (A + B).(A + C) (AND Distributive Law)
#Absorptive Law – This law enables a reduction in a complicated expression to a simpler one by absorbing like terms.
A + (A.B) = A (OR Absorption Law)
A(A + B) = A (AND Absorption Law)
#Associative Law – This law allows the removal of brackets from an expression and regrouping of the variables.
A + (B + C) = (A + B) + C = A + B + C (OR Associate Law)
A(B.C) = (A.B)C = A . B . C (AND Associate Law)
#Boolean #postulates #Algebra