Correct Answer - Option 4 : Neutral
Neutral function:
Neutral function in which a number of minterms are equal to the number of max terms.
The number of neutral function possible are \(~^{2^n}C_{2^{n-1}}\)
- For n variables, the total number of terms possible = number of combinations of n variables = 2n
- Since a maximum number of terms possible = 2n, so we choose half of the terms i.e 2n / 2 = 2n-1
- Thus, a number of neutral functions possible with n Boolean variables = C ( 2n, 2n-1 )
- The function does not contain two mutually exclusive terms.
Hence the option (4) is correct
Boolean function:
A Boolean function is described by an algebraic expression consisting of binary variables, the constants 0 and 1, and the logic operation symbols +, ., ‘
It may be noted that two levels of logic are minimum required to implement an arbitrary Boolean function.
Example = f(A, B) = AB’ + A’B is a Boolean function with two binary variables.
Self-dual function:
A function is said to be Self-dual if and only if its dual is equivalent to the given function, i.e.,
if a given function is f(A, B, C) = (AB + BC + CA) then its dual is, fd(A, B, C) = (A + B).(B + C).(C + A) (fd = dual of the given function).
In a dual function
AND operator of a given function is changed to OR operator and vice-versa.
A constant 1 (or true) of a given function is changed to a constant 0 (or false) and vice-versa.