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Self Dual Expression

Self  Dual Expression:

Before seeing this chapter please follows previous chapters: 

Neutral and Mutually Exclusive function,  Duality and Complementary

Definition: Self Dual expression is possible, when we take dual of a Boolean expression, we will get the same Boolean expression.

Example:

Dual of above expression:

Now if we simply it:

So, it is a self-dual function.

Some example like 

When a Boolean expression is self-dual:

A Boolean function is self-dual if

(i) It is a neutral function (no. of minterms = no. of maxterms). 

See Neutral and Mutually Exclusive Function

(ii) The function does not contain two mutually exclusive terms.

See Neutral and Mutually Exclusive Function

Let’s explains the two above conditions by an example: 

From above we know that AB + BC + CA is a self-dual expression because dual of this said expression is the same itself.

To know the above Boolean expression satisfying two conditions or not we convert it to canonical SOP. 

For more details see: Conversion To Canonical Form

Now, we see the above self-dual function satisfying two conditions or not:

If we want to write a truth table of the above function.

From the truth table it is clear that the number of minterms = the number of maxterms, so, it is a neutral function. 

See Neutral Function: Neutral and Mutually Exclusive Function

Now, in the above truth table, the mutually exclusive terms are:

(0, 7), (1, 6) , (2, 5) and (3, 4)

See Mutually Exclusive Function: Neutral and Mutually Exclusive Function

Now if we write the SOP (minterms) from the above truth table: 

Here 3, 5, 6, and 7 are not mutually exclusive terms.

So, the above function SOP (minterms) Y does not contain two mutually exclusive terms.

So, the above function SOP (minterms) 

Y = ABC + ABC’+ A’BC+AB’C = AB + BC + CA is self-dual function.