What does it mean by Canonical Form of Boolean Expressions?

It is very basic but very important question that what is a conical form of Boolean expression ? If we take any expanded Boolean expression where each term contains all Boolean variables in their true or complemented form, is also known as the canonical form of the expression.

Now take an example to understand the above statement,  F(A,B,C) = A^B^C^+ A^B^C+ ABC^ is a three variable function of Boolean expression. Now see in that Boolean expression, all of those three variables are present in complemented or un-complemented form. So we can say that the above Boolean expression is expressed in canonical form.

Now further if we go for simplification of that Boolean expression then we will get

 

A^B^C^+ A^B^C+ ABC^

= A^B^(C^+C)+ ABC^

=A^B^+ ABC^  ( Because C^+C = 1)

 

After simplification we get F(A,B,C)=A^B^+ ABC^. Now see it loos its conical form because in this expression all the three literal are missing in all terms.

 

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