SOP and POS Full Form

SOP stands for Sum-of-Products form and POS stands for Product-of-sums form. SOP and POS are different ways of the Boolean functions of digital circuits. A boolean Function is an algebraic form of Boolean expressions. Boolean expressions are an expression that consists of variables, constants, and logical operators. These Boolean expressions show the results in true or false in form of 0 (i.e., means true) and 1(i.e., means false).

This Story also Contains

1. Boolean Function Representation
2. Sum of Product (SOP) Form
3. SOP Method
4. Product of Sums (POS) Form
5. POS Method

Boolean Function Representation

As we say that in the boolean algebra 0 represents the false or open state of the logical gate and similarly, 1 is represented as the true or closed state of the logical gate.

Thus, a Boolean function is formed from an algebraic form of a boolean expression. It is represented by using NAND gates and also by using the K-Map (i.e., Karnaugh map) method through which it is standardized in two types of standard form:

1. SOP (Sum of Product form)

2. POS (Product of sum form)

Through the use of various Boolean laws and theorems, Boolean functions consist of three types of digital circuits such as:

• Sum-of-Products (SOP) form

• Product-of-Sums (POS) form

• Canonical forms (Standard SOP and POs Form)

Sum of Product (SOP) Form

The sum-of-products (SOP) form is a form of boolean expression of logical gates in simplifying the method of Boolean Representation functions. In this form, the variables are operated by the AND gate (product) to find the results of product functions and OR gate (sum) to find the results of sum functions.

It is also known as the Disjunctive Normal Form and Standard SOP.

In the SOP form of Boolean Representation Functions, all the variables which are used are operated by AND (product operators) which forms product terms, and then all these product terms are added together by OR (sum operators) to the final results of the given Boolean Expression.

Sum-of-products form represented in its best form by using FPGA (Field Programmable Gate Arrays).

SOP Method

SOP form can be formed by this:

• To produce a HIGH output, write an AND term for each combination of each input.

• Write the input variables if the given value is 1, and the complement of the variable if the given value is 0.

• The output function is obtained in terms of OR the AND terms.

Product of Sums (POS) Form

The product-of-sums (POS) form is a form of Boolean expressions of logical gain which uses the simplifying method of Boolean Representation functions. It is also called Conjunction Normal Forms and Standard POS.

Similarly here also as SOP, the variables are operated by the AND gate (product) to find the results of product functions and OR gate (sum) to find the results of sum functions.

In the POS form of Boolean Representation Function, all the variables which are provided in Boolean expression are firstly summed together (by OR operator) and then multiplied together (by AND operator) to get the final answer. This is also known as the Dual of SOP Form.

POS Method

POS form can be obtained through this method:

• To produce a LOW output, write an OR term for each combination of each input.

• Write the input variables if the given value is 0, and the complement of the variable if the given value is 1.

• The output function is obtained in terms of AND the OR terms.