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Examples: Self Dual Function

Before seeing this chapter please follows previous chapters:

Self Dual Expression, Number of Self-Dual Function

How many questions can occur from self-dual function and related to self-dual function?

Type 1:

Example 1:

How many Boolean functions with n variables are self-dual?

Solution:

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

For more details please follow: Number of Self-Dual Function

Option (c) is the correct answer.

Example 2:

How many self-dual functions are possible with 3 variables?

(a) 256     

(b) 6      

(c) 8     

(d) 16

Solution:

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

For more details please follow: Number of Self-Dual Function

Option (d) is the correct answer.

Type 2:

Example:

Which type of function is the neutral function where the number of variables is A,B, and C?

Before seeing the example please follows: 

Neutral and Mutually Exclusive Function

Solution:

The neutral function is those where the number of minterms and maxterms are equal.

A function is called neutral function where the number of minterms = the number of maxterms.

For three variables (3) number of total terms possible are 

Within 8 total terms, those function is called neutral function where 4 minterms and 4 maxterms are present. 

Option (a) is incorrect because here number minterms are 5 

Option (b) is correct because here number minterms are 4 

Same like option (a), option (c), and option (d) has not had an equal number of minterms and  maxterms so, both are also not a neutral function.

So, option (b)  is the correct answer.

Type 3:

Example:

In following all functions which one is not mutually exclusive? 

Before seeing the example please follows: 

Neutral and Mutually Exclusive Function

Solution:

A function is called a mutually exclusive function if a term and complement of this term are present in this function at the same time. 

In this case function F(A, B, C) are mutually exclusive.

From the truth table, we can define mutually exclusive like:

So, in the above truth table, the mutually exclusive terms are:

(0, 7), (1, 6) , (2, 5) and (3, 4)

If any pair is present in the function then this function is called mutually exclusive function.

Option (a) is incorrect 

Option (b) is incorrect

Option (c) is correct

Option (d) is incorrect

So, option (c) is the correct answer.

Type 4: 

Example:

In following all functions which one is self-dual? 

Solution:

(i) It is a neutral function (no. of minterms = no. of maxterms). 

See Neutral and Mutually Exclusive Function

(ii) The function does not contain two mutually exclusive terms. 

See Neutral and Mutually Exclusive Function

Examples:

If we want to write a truth table of the above function.

From the truth table, it is clear that the number of minterms = the number of maxterms, so, it is a neutral function. 

See neutral function: Neutral and Mutually Exclusive Function

Now, in the above truth table, the mutually exclusive terms are: 

(0, 7), (1, 6), (2, 5) and (3, 4)

Option (a) is incorrect

Option (b) is correct 

Option (c) is incorrect

Option (d) is incorrect