Boolean Postulates and Theorem Digital Logic and Computer Design by Ravinder Nath Rajotiya - September 22, 2022December 16, 20220 BOOLEAN POSTULATES and THEOREM Boolean algebra was introduced by George Boole in 1854. Boolean algebra is used to perform binary and logical operations and differs in this respect from the ordinary algebra. Postulates of Boolean Algebra 1. Identity Law : A + 0 = A A.1 = A 2. Commutative Law: (A+B) = (B+A) A.B = B.A 3. Associative Law: A + (B + C) = (A + B) + C A.(B.C) = (A.B).C 4. Distributive Law: A . (B + C) = A.B + A.C A + (B.C) = (A + B). (A + C) 5. Complement Law: A+A’ = 1 A.A’ = 0 Boolean Algebra Theorems 1. Duality Theorem: It states that we can derive a Boolean relation from another Boolean relation by just : i. Changing the ‘.’ With a ‘+’
Boolean Theorems STLD/Digital Electronics by Ravinder Nath Rajotiya - August 6, 2019May 10, 20210 Duality Principle: Dual of an expression can be obtained by : Changing all + with . Complement 0’s and 1’s i.e. 1’=0 and 0’=1 Keep the variable sam (i.e. do not complement the variable) Example: Find the dual of : A(B+C) = AB + AC Solution: Find the Dual of F(xyz)=(x+y) (x+z)(y+z) Solution: (x+y) (x+z)(y+z) = (xx+xz+xy +yz)(y+z) = (x+xz+xy+yz)(y+z) = (x +xy +yz )(y+z) = (x+yz)(y+z) = xy +xz + yyz + yz = xy + xz + yz Also dual of (x+y) (x+z)(y+z) = xy + xz + yz Therefore, we find that in this case dual of a function is the function itself 3. For n variables expression haw many total dual functions are possible Solution: Which of the following is TRUE S1: The dual of NAND function is NOR S2:The dual of