# Product-of-Sums (POS) Form

A logic expression consisting of sum (OR) terms that are the factors of a logical product (AND) is said to be of the product-of-sums (POS) form.

Used when the output is 0. Sum of Products used when the output is 1.

POS Form and SOP Form are logically equivalent.

### Converting a Sum Term to Standard POS

Step 1. Add to each nonstandard product term a term made up of the product of the missing variable and its complement. This results in two sum terms. As you know, you can add 0 to anything without changing its value. Step 2. IMPORTANT: Apply rule 12 from Table 4-1: A + BC = (A + B)(A + C) Step 3. Repeat Step 1 until all resulting sum terms contain all variables in the domain in either complemented or noncomplemented form.