SOP Vs POS

SOP and POS are two of the important topics of the Boolean algebra. SOP refers to the sum of the product of the minterms, whereas POS is the Product of the sum of terms. SOP and POS help us simplify the complex Boolean variables and are mainly used in K-maps. In this article, we will explore the difference between SOP and POS. Let’s start learning on the topic of SOP vs POS.

What is SOP?

The SOP stands for Sum of Products defined as the sum of minterms. As the name suggests the SOP form represents the OR operation of the product terms i.e., minterms. The SOP represents the minterms in the Boolean algebra. The SOP is denoted by ∑. As the SOP deals with the minterms it works on active high logic.

Example of SOP

• AB + CD
• P’Q + R
• X’Y’ + W’Z’

SOP in K-Map

The below image represents the SOP in K-map.

SOP in K-Map

What is POS?

The POS stands for Product of Sum defined as the product of maxterms. As the name suggests the SOP form represents the AND operation of the sum terms i.e., maxterms. The POS represents the maxterms in Boolean algebra. The POS is denoted by Π. As the POS deals with the maxterms it works on active low logic.

Example of POS

• (A + B).(C + D)
• (P’ + Q).(R + S’)

POS in K-Map

Below image represents the POS in K-map.

SOP vs POS

Characterization	SOP	POS
Definition	SOP is sum of the minterms.	POS is the product of maxterms.
Stands for	SOP stands for Sum of Product.	POS stands for Product of Sum.
Representation	It represents minterms.	It represents maxterms.
Logic	It works on active high logic.	It works on active low logic.
Denotation	It is denoted by Σ.	It is denoted by П.
Output	The output of SOP is 1.	The output of POS is 0.

Learn more about minterm, maxterm and K-map

• Minterm vs Maxterm
• K-map

FAQs on SOP and POS

Q.1: Why are SOP and POS used for?

Answer:

SOP and POS are the standard forms used in K-maps for minimization of Boolean functions.

Q.2: What are two standard forms to represent Boolean functions in K-map?

Answer:

The two standard forms to represent Boolean functions in K-map are:

• SOP (Sum of Product)
• POS (Product of Sum)

Q.3: What is SOP?

Answer:

The SOP is the sum of the minterms used in K-maps to minimize the Boolean functions.

Q.4: The POS works on which logic?

Answer:

The POS works on active low logic i.e., the functions of the POS form work on 0 logic.