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Q: GATE 2014 CSE 

is the same expression as that of F with and swapped. F is said to be self-dual if with + and swapped. 

The number of self-dual functions with n Boolean variables is

Before seeing the answers please follow previous chapters: 

Self Dual Function, Number Of Self-Dual Function, Important Examples: Self Dual Function

Solutions:

See the definition of self-dual: Self Dual Function

For n variable how many self-dual functions are possible:

So, the number of mutually exclusive pairs are exactly half of the maximum possible minterms or maxterms

Now as we know from above every mutually exclusive pair has two choices to form a self-dual function.

So, total self-dual functions are possible 

For n variables, maximum numbers of possible Self-dual expressions are:

∴ Option (d) is the correct answer.

Q: UGC NET: 2013, Dec-Paper-2, Question-31

The dual of a Boolean expression is obtained by interchanging

a) Boolean sums and Boolean products

b) Boolean sums and Boolean products or interchanging 0’s and 1’s

c) Boolean sums and Boolean products and interchanging 0’s and 1’s

d) Interchanging 0’s and 1’s

Before seeing the answer please follows previous chapters: 

Duality and Complementary

Solution:

How dual an expression:

1. Change AND by OR and OR replace by AND.  (AND ↔ OR)

2. 1 replaced by 0 and vice versa.  (1 ↔ 0)                  

3.  Keep all literals as same.

Example:

Dual of above expression:

Note: There is no change in complement.

So, option (c) is the correct answer.

Q: UGC NET 2014, June, Paper-2, Question-17

How many Boolean functions of degree n are self-dual?

Before seeing the answers please follow previous chapters: 

Self Dual Function, Number Of Self-Dual Function, Important Examples: Self Dual Function

Solutions:

See the definition of self-dual: Self Dual Function

For n variable how many self-dual functions are possible:

So, the number of mutually exclusive pairs are exactly half of the maximum possible minterms or maxterms

Now as we know from above every mutually exclusive pair has two choices to form a self-dual function.

So, total self-dual functions are possible 

For n variables, maximum numbers of possible Self-dual expressions are:

∴ Option (d) is the correct answer.