Convert POS to Standard POS Form

This post was created and published to answer the following question:
"How to convert any given boolean expression in POS form into its equivalent boolean expression in standard POS form?"

But before we get started, let's spend a few moments going over the POS form. The following is an explanation of its meaning:

Literals are considered to be sum terms when using Product of Sum (POS) form, and then all of the sum terms are ANDed together to get the expression in POS form.

In a nutshell, POS consists of sum terms that are ANDed together to form the final product. In this case, each sum term might include one or more literal items or variable components. And literals can be in the form that complements them or the form that does not complement them. As an illustration, the expression can be written in POS form as follows:

(A'+B'+C).(A+B).(B'+C).(A+B+C')

To learn more about it, you can refer to its separate article. Now that we've gotten that out of the way, let's discuss the topic at hand, which is the transition from POS to SPOS.

POS to SPOS Conversion Steps

Here is a list of some rules that have to be followed for the conversion of any boolean expression from POS to standard POS form:

  • Find the missing literal for each sum term.
  • Now join the missing literals (in uncomplemented form) and missing literals (in complemented form) with AND operator, and then join this term with the sum term using OR operator.
    Or, in other words, OR each term combined with the term formed by AND including the omitted literal and its complement.
  • Repeat the process for all the sum terms that have missing literals.
  • Simplify the expression to get the boolean expression in standard POS form.

Let's use an example to put all of the above steps into practice and understand how to convert any given logical expression into standard POS form.

We have to convert the boolean expression.

F(A,B,C) = (A+B).(A+C).(A+C')

into its standard POS form.

We have C, B, and A, which are the three variables that are missing from the first, second, and third sum terms, respectively.

Now OR each term with the missing variable and its complement. After applying this rule, we get:

F(A,B,C) = (A+B+CC').(A+C+BB').(B+C'+AA')

Simplify the above boolean expression. Here is the simplification of the boolean expression:

= (A+B+CC').(A+C+BB').(B+C'+AA')
= (A+B+C).(A+B+C').(A+C+B).(A+C+B').(B+C'+A).(B+C'+A')
= (A+B+C).(A+B+C').(A+B'+C).(A'+B+C)

Therefore, the logical expression is:

(A+B).(A+C).(B+C')

in standard POS form are:

(A+B+C).(A'+B+C).(A+B'+C).(A+B+C')

And finally, the function in standard POS is defined as:

F(A,B,C) = (A+B+C).(A'+B+C).(A+B'+C).(A+B+C')

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