Expression Form Types

We've seen that expressions may have several equivalent forms.

To prevent confusion, computer scientists prefer to stick to specific types of forms which they call standardized or canonical forms. These types include:

• The sum-of-products form, e.g. $E = xy + x'y'$.
  • It's an expression of ANDed variables that are then ORed together.
• The product-of-sums form, e.g. $E = (x + y')(x'+ y)$.
  • It's an expression of ORed variables that are then ANDed together.

The following is true and very useful to know:

• Every expression can be written in a sum-of-products form a unique product-of-sums form.
• The sum-of-products form is easier and preferred over the product-of-sums form.
• One can easily use an expression's truth table to write its sum-of-products form.