# Difference between the SOP and POS in Digital Logic

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The Difference between the SOP and POS in Digital Logic is that the SOP includes the OR of multiple product terms. POS, on the other hand, generates a logical expression composed of the AND of multiple OR terms. The SOP (Sum of Product) and POS (Product of Sum) methods are used to deduce a specific logic function.

Difference Between SOP and POS in Digital Logic PDF

In other words, SOP and POS are the representations of the deduced reduced logic function. The deduced logic function can be used to design a logic circuit. In this article, we see the difference between the SOP and POS in Digital Logic before that, we dive further individually into SOP and POS forms.

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## Difference Between SOP and POS in Digital Logic

The difference between SOP and POS is essential for the upcoming GATE exam. The table below shows a comparison of SOP vs. POS in Digital Logic based on expression, including a method of representation, etc.

### Key Differences Between SOP and POS in Digital Logic

 SOP POS SOP is useful for representing Boolean expressions as a sum of product terms. POS is useful for representing Boolean expressions as a product of sum terms. SOP employs minterms. POS employs max terms. Minterm can be considered a Boolean variable product (in normal or complemented form). Minterm can be considered a Boolean variable sum (in normal form or complemented form). SOP is computed as the sum of the minterms. POS is computed as the product of the max terms. Minterms are represented by the letter ‘m.’ Max terms are represented by the letter ‘M’ It is formed by considering all of the minterms whose output is HIGH (1). It is formed by considering all of the max terms whose output is HIGH (0). When minterms are written for SOP, input with value 0 is treated as the input’s complement. When max terms are written for POS, input with value 0 is treated as the variable.

## What is SOP?

The sum-of-products (SOP) form is a method (or form) for simplifying logic gate Boolean expressions. The variables are AND (summed or added) together to form a product term in this Boolean function representation SOP form.

A sum-of-products form can be created by adding (or summing) two or more product terms using a Boolean addition operation. Based on the SOP, various questions can be formulated in the GATE CSE question paper. The product terms are defined using the AND operation, and the sum term is defined using the OR operation.

The sum-of-products form is also known as the Disjunctive Normal Form because the product terms are ORed together, and the Disjunction operation is logical OR. The sum-of-products form is also known as Standard SOP.

## What is POS?

The product of sums form is a method (or form) of simplifying logic gate Boolean expressions. It carries a good marks weightage in the GATE CSE syllabus. All variables in this POS form are ORed, i.e., written as sums to form sum terms.

The product-of-sum form is obtained by ANDing (multiplying) all of the sum terms together. This form is the polar opposite of the SOP form. As a result, this is also known as the Dual of SOP form. SOP

The sum terms are defined using the OR operation, while the product terms are defined using the AND operation. When two or more sum terms are multiplied by a Boolean OR operation, the resulting output expression is in product-of-sums form, also known as POS.

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