Summery of Logic Gates


The (axioms) rules of Boolean Algebra are:
  • AND Operations (•)

    • 0·0 = 0     A·0 = 0
    1·0 = 0     A·1 = A
    0·1 = 0     A·A = A
    1·1 = 1     A·A' = 0
  • OR Operations (+)

    • 0+0 = 0     A+0 = A
    1+0 = 1     A+1 = 1
    0+1 = 1     A+A = A
    1+1 = 1     A+A' = 1
  • NOT Operations ( ' )

    • 0' = 1     A' = A
    1' = 0

Commutative Law Associative Law
A·B = B·A
A+B = B+A
 (A·B)·C = A·(B·C) = A·B·C
(A+B)+C = A+(B+C) = A+B+C

Distributive Law
Idempotent Law
A·(B+C) = (A·B) + (A·C)
A+(B·C) = (A+B) · (A+C)
A·A = A
A+A = A

DeMorgan’s Theorem
(A·B)' = A' + B' (NAND)
Not A and B is combined operator which is called NAND
(A+B)' = A'·B' (NOR)
Not A or B is combined operator which is called NOR

Virtual Labs - Logic Gates
(Resources from Internet)

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