Self Dual and Neutral Function in digital electonics

Question

I have seen this concept in one of the test series then i referred morris mano but not able to find  this concept.

I looked at some online definitions (One of them is https://gateoverflow.in/1958/gate2014-2_6)  and people are defining it like:-

Self Dual Function has two properties:-

1. No. of maxterms=no. of minterms (Neutral functions)

2. No mutually exclusive terms

Now second point i understand ,but what is netutral function saying in 1st point?I think every boolean funciton on n variables has n 2^n minterms and 2^ n maxterms,so always number of minterms and number of maxterms are same.So what exactly is neutral function?Is every boolean function is neutral function?

or it it like the number  minterms which are 1 =number of maxterms which are 0?

If we simply say number of minterms=number of maxterms then it is always true i guess.Please clariffy.Also suggest me some book to read these two concepts?

Alos let me know  If someone says minterm,does that mean that fxn o/p is one for that minterm?

Comments

Some of those definitions are not standard - you can read this now:

https://gateoverflow.in/1958/gate2014-2_6

---

Nice doubt bro

---

What do u mean by mutually exclusive term first time heard and what does it mean

Answer 1

Minterm: A product term which contains each of 'n' variable as factors either in complemented or uncomplemented form is called minterm. For ex: 3 variable function ab^cc is a minterm but not ab (as this product term doesn't contains all the 3 term).

Canonical Sum of Products: The Sum of all minterms of function 'f' for which 'f' assumes '1' is called Canonical sum of products or disjunctive normal form.

Maxterm: A sum term which contains each of 'n' variable as factors either in complemented or uncomplemented form is called minterm. For ex: 3 variable function (a + b^c  + c) is a maxterm but not (a + b).

Canonical Product of Sums: The product of all maxterms of function 'f' for which 'f' assumes '0' is called Canonical product of sums or conjunctive normal form.

Neutral Function: Neutral function are the function having no. of minterm in Canonical SOP is equal to no. of maxterm in Canonical POS.

Self dual function: If the dual of a function is equal to the function. Then the function is called self dual. A dual function is obtained by interchanging every '.' and '+'.

A Boolean function is self dual function if

1. It is neutral function.

2. The function does not contain mutually exclusive terms.

More ever, The Canonical sum of products or Product of sums of a Switching function is unique. Means for a function you will have only one Canonical SOP.

These definition may not be standard. But these are what i have learned. So if anyone is wrong correct it.

Answer 2

See this example :

  A    B  F1  F2  F3  F4  F5 F6

  0     0   0    1   1     0   1    0

  0     1   0    1   0     1    0   1

  1      0  1    0   1     0    0   1

  1      1  1    0   0     1    1   0

function output is such that it is zero for half of the input(maxterm),and 1 for the rest half(minterm).If we have n variable then (2^n)C(2^(n-1)) functions are there which are neutral.

Comments

That is fine. But I am asking is it true that neutral fan has Number of minterms =number of maxterms? Or it should be as I mentioned in my question above

---

I think in minterm only those combination are taken,whose values are 1,and in maxterm only those ,whose values are 0. Otherwise it should be mentioned. I find your point friend.