# GATE1989-4-x

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Provide short answers to the following questions:

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).

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  $2^{n} \choose 2^{n-1}$.

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