GATE CS 2014 Set 2 — Question 16
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Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems
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Question
The dual of a Boolean function , written as , is the same expression as that of with and swapped. is said to be self-dual if . The number of self-dual functions with Boolean variables is
Correct answer
(D) 2^2ⁿ⁻¹
Solution
A Boolean function is self-dual if .
This condition implies that for every input combination , the output
For each pair, we have 2 choices for the output values (either or ).Since there are such pairs, the total number of self-dual functions is:
This condition implies that for every input combination , the output
F(X) determines the output for the complementary input . Specifically, .There are possible input combinations. These can be grouped into pairs of mutually complementary inputs .For each pair, we have 2 choices for the output values (either or ).Since there are such pairs, the total number of self-dual functions is:
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