Convert SOP to Standard SOP Form

In this tutorial, we will learn how to convert any given boolean expression in SOP form to its equivalent boolean expression in standard SOP form.

However, before we get started, it will be beneficial for us to first gain an understanding of what the SOP form is all about. Therefore, let's not waste any more time and immediately begin by providing a concise definition of it.

In the SOP form, the sum and product are not the actual results of addition or multiplication. They are, rather, the OR and AND functions. The SOP is only concerned with 1. It is unconcerned about the value 0.

The SOP form is used to generate boolean expressions from truth table data.

A B F
0 0 1
0 1 1
1 0 0
1 1 0

The two literals or variables in this case are A and B, and the function is denoted by the letter F.

It is called the SOP form because it contains the sum of product terms. For example, if A, B, and C are three literals or inputs of any combinational circuit and Y is the function, then the SOP expression may be written as given below:

Y = ABC + AB'C + AC

Or

Y = A'BC + B'C + A'C'

etc. are some of the examples of SOP boolean expressions. I will not go into detail about it; however, if you would like more information regarding the "SOP" form, you can refer to its own separate article. Let's move on to the meat of the discussion, which is the process of converting sum-of-product (SOP) values to standard sum-of-product (SSOP) values.

Steps for Converting SOP to SSOP

Here are some of the steps that have to be followed to convert any logical expression into standard SOP form:

  • Find the missing literals or variables for each and every product term. For example, C is the missing term from the three variable boolean expressions' product term AB.
  • Apply the OR operator between the missing literal and its complement. For example, (C+C')
  • Now join it with the product term through the AND operator. For example, AB(C+C')
  • Repeat all the above steps, that is, from step 1 to step 3, to apply to all the product terms that have missing literals or variables.

Now let's take an example to understand it in a practical way to apply the above steps:

F(A,B,C) = AB + AC' + BC

Here, the first term is AB, the second term is AC, and the third term is BC. We have three product terms, each with one variable missing.

In the first, second, and third terms, the variables C, B, and A are missing, respectively.

Now, to perform the conversion, follow the above steps for the conversion purpose. After performing the above steps for all the product terms that have a missing variable (here all the terms have a missing variable), initially we will get the following expression:

F(A,B,C) = AB(C+C') + AC'(B+B') + BC(A+A')

Now simplify the above expression as given below:

= AB(C+C') + AC'(B+B') + BC(A+A')
= ABC + ABC' + ABC' + AB'C' + ABC + A'BC
= ABC + ABC' + AB'C' + A'BC

Therefore, in standard SOP form, the final function will be:

F(A,B,C) = ABC + A'BC + ABC' + AB'C'

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