write the dual of
AB+BC+CA’+B’C’
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Self-Dual Functions | Dual Of Boolean Expression
Digital Design
Dual Of Boolean Expression-
To get a dual of any Boolean Expression, replace-
OR with AND i.e. + with .
AND with OR i.e. . with +
1 with 0
0 with 1
Dual of Boolean Expression Examples-
Following are examples of dual of Boolean Expressions-
Example-01:
Consensus theorem is xy + x’z + yz = xy + x’z
Dual of Consensus theorem is (x + y)(x’ + z)(y + z) = (x + y)(x’ + z)
Example-02:
Boolean expression is xyz + x’yz’ + y’z = 1
Dual of the above Boolean expression is (x + y + z)(x’ + y + z’)(y’ + z) = 0
Self-Dual Functions-
When a function is equal to its dual, it is called as a Self dual function.
Example-
Consider the function : F (A , B , C) = AB + BC + CA
The dual of this function is-
Fd (A , B , C)
= (A + B)(B + C)(C + A)
= AB + BC + CA
Clearly, F (A , B , C) = Fd (A , B , C)
∴ F (A , B , C) is a self-dual function.
Conditions For Self-Dual Function-
The necessary and sufficient conditions for any function to be a self-dual function are-
The function must be a Neutral Function.
The function must not contain any mutually exclusive terms.