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While considering the digital logic and user input, several data, desires, and output. However, a digital logic’s input and output functions are processed through binary numbers, also called boolean values. These boolean values are either zero or one. Therefore, when it comes to the boolean logic, these zeros and one race a digital signal which gives the desired output. Therefore these signals, raised within a boolean expression, can be represented in two ways. They are
- SOP, also called the Sum of products.
- POS, which is also termed the Product of sums.
Moreover, the input variables are termed ‘n’ when the boolean logics are considered. Therefore, the combination of the algebraic version of the boolean will be 2n,,,,. Under this assumption, the value of 0, is considered LOW, representing one of the compliments, whereas the value of 1 is considered HIGH, representing the higher compliment.
What is SOP?
The Sum of products is considered one of the ways of raising a signal within a boolean expression. Considering the operations used within a boolean calculation, AND operation is used to give out the logical product of the boolean expressions. In contrast, OR operation is used to give out the logical Sum of the boolean expression. Therefore, the Sum of products combines both OR operation and AND operation. The Sum of a product is used to identify and express the combinational logic of more than one product, which are summed together. In simple terms, the Sum of a product can be defined as constituting the products by using the AND function and then summing them all together using the OR function. A simple example of the Sum of products is given below:
Q= (A.B) (A.C) (C.B).
Moreover, the product terms of these SOP are also called min-terms.
What is POS?
The POS stands for product of sums. Therefore, the name itself suggests the overall functioning of POS, which means it performs the multiplication of the summed-up elements or the boolean values. As the product terms of SOP were called mini terms, similarly, in POS, the product terms are called max terms. Therefore, the sequence of the operations undertaken through the boolean logistics is equivalent to the end organ function of the product of sums. According to logical terms, the basic output and the result of more than one OR function are constituted into a product and are connected through the And function.
A general representation of the product of sums is as follows:
Q= (A B). (B C). (C A)
However, most of the bullet expressions considered under the product of Sum are of a nonstandard form. However, they can be converted into the standard form using the distributive law.
Difference between SOP and POS:
SOP and POS are expressive variants of the boolean logistics. However, there are several differences associated with each of them. The tabular representation of the differences between SOP and POS follows
| SOP | POS. |
| It is used to represent the expressions in terms of the Sum of the product. | It is used to represent the expression of the terms of the Sum product. |
The terms that are used under SOP are called minterms. Moreover, these terms are also presented in either normal or complemented forms. | The terms that are used under POS are called max terms. Moreover, these terms are also presented in either normal or complemented forms. |
| The representation of the output of SOP and its min-term is done by ‘m’. | The output of POS and its max term is Represented by ‘M’. |
| While considering the product of the minterms and their Sum of products, the overall need to be HIGH, i.e., 1. | While considering the product of the Max term under the product of sums, the overall output needs to be LOW, i.e., 0. |
| When writing them in terms of some products, the input value, 1, is considered the variable. On the other hand, the value 0 is considered a compliment. | When writing the Max term of products of sums, the input value, 0, is considered the variable. On the other hand, the value one is considered a compliment. |
