GATE CSE 1989 | Question: 4-x

Question

A switching function is said to be neutral if the number of input combinations for which its value is $1$ is equal to the number of input combinations for which its value is $0.$ Compute the number of neutral switching functions of $n$ variables (for a given $n$).

Comments

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Answer 1

For an 'n' variable function, total number of possible minterms(input combinations) will be $2^n$. Half of them will be one i.e, $2^{n-1}$.

Thus total number of neutral functions possble = Choosing any $2^{n-1}$ combinations to be 1 out of $2^n$ combination. i.e  $2^{n} \choose 2^{n-1}$.

Comments

Self dual function https://math.stackexchange.com/questions/1602598/number-of-self-dual-functions-and-number-of-inputs-for-which-self-dual-function

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Note that question is not asking for number of self dual functions.

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In such a questions best way to cross check is take 1 or 2 variable function & verify it.