Maximum number of Self Dual possible for 4-variable function

Explanation:
To understand the maximum number of self-dual functions possible for a 4-variable function, we need to first understand what a self-dual function is.

A self-dual function is a Boolean function that remains unchanged when the input variables are complemented. In other words, if we invert all the input variables, the function should remain the same.

Properties of self-dual functions:
1. The number of 1s in the truth table is equal to the number of 0s.
2. The number of minterms is equal to the number of maxterms.

Truth table for a 4-variable function:
A 4-variable function can have a total of 2^4 = 16 possible combinations of inputs. Let's consider the truth table for a 4-variable function:

A | B | C | D | F
-----------------
0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
1 | 1 | 1 | 1 |

Maximum number of self-dual functions:
To find the maximum number of self-dual functions possible for a 4-variable function, we need to count the number of functions that satisfy the properties of self-duality.

1. The number of 1s in the truth table is equal to the number of 0s. In a 4-variable truth table, there are 2^4 = 16 total possible combinations. Therefore, there must be 8 1s and 8 0s in the truth table.

2. The number of minterms is equal to the number of maxterms. In a 4-variable function, there are 2^4 = 16 total possible minterms and 2^4 = 16 total possible maxterms. Therefore, the number of minterms must be equal to the number of maxterms, which is 16.

Conclusion:
Based on the properties of self-dual functions, we can conclude that the maximum number of self-dual functions possible for a 4-variable function is 256.