In this note, we are going to know about the Logical Expression of SOP and POS in Digital Electronics. Welcome to Poly Notes Hub, a leading destination for diploma or polytechnic Notes.

Author Name: Arun Paul.

Logical Expression of SOP and POS in Digital Electronics

Logical functions are typically expressed in terms of logical variables. Logical functions and variables take on binary values. An arbitrary logic function can be stated in the following ways:

• Sum of Products or SOP Form
• Product of Sums or POS Form

Product Term

The AND function is known as a product. In Boolean algebra, the term “product” loses its original meaning but is used to denote an AND function. A product term is the logical product of multiple variables on which a function is based. The variables in a product term can be either complemented or uncomplemented. ABC̅ is a product term.

Sum Term

A sum is commonly denoted by the OR function (+ symbol). A sum term is defined as the logical sum of multiple variables on which a function depends. Variables in a sum term can take either complemented or uncomplemented form. A + B̅ + C represents a sum term.

What is Sum of Products or SOP Form?

The logical sum of two or more logical product terms is called a Sum of Products expression. It is basically an OR operation of AND operated variables.

Here we have listed some SOP Forms of Logical Expressions

Basic SOP examples

1. Y = AB + C
2. Y = A̅B + BC̅ + AC
3. Y = A̅B̅ + AB
4. Y = ABC + A̅B + BC
5. Y = A̅B̅C + AB̅ + AC̅

Standard SOP examples (all terms contain all variables)

1. Y = A̅B̅C + A̅BC̅ + ABC
2. Y = A̅BC + AB̅C + ABC̅ + ABC

What is Product of Sums or POS Form?

A product of sums expression is a logical product of two or more logical sum terms. It is basically an AND operation of OR operated variables.

Here we have listed some POS Forms of Logical Expressions

Basic POS examples

1. Y = (A + B)(B + C̅)
2. Y = (A + C)(A̅ + B + C̅)
3. Y = (A̅ + B)(A + C)
4. Y = (A + B + C̅)(A̅ + C)
5. Y = (A + B)(A̅ + C̅)(B + C)

Standard POS examples (each sum term contains all variables)

1. Y = (A + B + C)(A + B̅ + C̅)(A̅ + B + C)
2. Y = (A̅ + B + C̅)(A + B̅ + C)(A + B + C̅)