Min Max Terms and Canonical Forms

In this class, We discuss Min Max Terms and Canonical Forms.

The reader should know about elementary sum, product, and normal forms. Click Here.

Minterms:

First, we understand minterms and max terms.

Take two variables, P and Q.

The below diagram shows the truth values for the two variables.

Using the truth values, we write the minterms.

True is written as p, and false is written as ¬p.

The minterms are (p ∧ q), (p ∧ ¬q), (¬p ∧ q), and (¬p ∧ ¬q).

Similarly, we have eight minterms for three variables.

The diagram below shows the truth values and the minterms.

The eight minterms are (p ∧ q ∧ r), (p ∧ q ∧ ¬r), (p ∧ ¬q ∧ r), (p ∧ ¬q ∧ ¬r), (¬p ∧ q ∧ r), (¬p ∧ q ∧ ¬r), (¬p ∧¬ q ∧ r), and (¬p ∧¬ q ∧ ¬r)

Max Terms:

In the maxterms we use disjunction instead of conjunction.

The maxterms for two variables are (p ∨ q), (p ∨ ¬q), (¬p ∨ q), and (¬p ∨ ¬q).

Canonical forms:

1) Canonical sum of products

2) Canonical product of sums.

The canonical sum of products or principal disjunctive normal form.

For a given formula, an equivalent formula containing a disjunction of minterms is only then called the canonical sum of products.

Example: (¬p ∧ q) ∨(p ∧ q)

Canonical product of sum or principal conjunctive normal form.

For a given formula, an equivalent formula containing conjunction of maxterms only then we call the canonical product of sum.

Example: (p ∨ q) ∧ (¬p ∨ q)