Difference Between SOP and POS


SOP (Sum of Product) and POS (Product of Sum) are the methods of representing a reduced logic expression. The basic difference between the two is that SOP expresses a Boolean function as a sum (logical OR) of product (logic AND) terms, while POS expresses a logic function as a product (logic AND) of sum (logic OR) terms.

Read this article to learn more about SOP and POS and how they are different from each other.

What is SOP?

Sum of Product (SOP) is a method of representing a logic function by using minterms. The expression of a SOP includes product terms which are taken where the input set gives a value HIGH (1).

In SOP, the value (HIGH) "1" represents the variable, while the value (LOW) "0" represents the complement of the variable. The final logic expression is obtained by adding (ORing) all the product terms (called minterms). Therefore, the implementation of Boolean function requires OR gate after the AND gates.

What is POS?

Product of Sum (POS) is a method of defining a logic function by using maxterms, i.e. product of sum terms. In the case of POS, the maxterms are represented by 'M'.

In POS, the value "0" represents the variable, while the value 1 represents the complement of it. The final Boolean expression is obtained by multiplying (ANDing) all the sum terms (maxterms). Hence, when the output Boolean function is implemented, it requires AND gate after the OR gates.

Now, let us discuss the differences between SOP and POS in detail.

Difference between SOP and POS

The following table highlights all the important differences between SOP and POS −

S.No.

SOP (Sum of Product)

POS (Product of Sum)

1.

It helps represent Boolean expressions as sum of product terms.

It helps represent Boolean expressions as product of sum terms.

2.

It uses minterms.

It uses maxterms.

3.

Minterm can be understood as a product of Boolean variables (in normal form or complemented form).

Maxterm can be understood as the sum of Boolean variables (in normal form or complemented form).

4.

It is calculated as the sum of minterms.

It is calculated as the product of maxterms.

5.

Minterms can be represented using the letter 'm'

Maxterms can be represented using the letter 'M'

6.

It is formed by taking into consideration all of minterms, whose output is HIGH (1).

It is formed by taking into consideration all of the maxterms, whose output is LOW (0).

7.

When minterms are written for SOP, input that has value 1 is considered as the variable.

When maxterms are written POS, input that has value 1 is considered as the complement.

8.

When minterms are written for SOP, input that has value 0 is considered as complement of the input.

When maxterms are written for POS, input that has value 0 is considered as the variable itself.

Conclusion

The most significant difference between the two is that SOP uses minterms, while POS uses maxterms.

Updated on: 22-Feb-2023

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