#gate #digital logic #neutral function #derivation

Question

How formula of neutral function is derived? I get that it has equal number of max and min terms but didnt get derivation

Comments

Which formula you didn’t get ? No of neutral function ?

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ya

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The defination of neutral function is those function which has equal number of Maxterm and minterm.

Now ,

We have $n$ variables so total number of combination possible is $2^{n}$.

No it will be a neutral function if output of half these combination is 1 and half of these combination is 0 which implies no of Maxterm is equal to no of minterm.

So we need half of the total combination means

$2^{n-1}$ is Maxterm and rest $2^{n-1}$ is minterm.

So this is same as selecting $2^{n-1}$ combination from total $2^{n}$ .

So with $n$ variable total number of neutral function is $\binom{2^{n}}{2^{n-1}}$

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Hopefully, you might get some insight about derivation from this video –>

Watch from 1:03 till the end.