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_______ is a function for which the number of minterms and number of maxterms are same.
1. Boolean
2. Universal
3. Self dual
4. Neutral

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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.

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