Convert Standard POS to Minimal POS form

This article was created and published to answer the following question:
"How to convert any given logical expression in standard POS (Product of Sum) form into its equivalent logical expression in minimal POS form?"

Before we get started, here are two posts that we think you'll find interesting and that we recommend you check out:

• Product of Sum (POS)
• POS to Standard POS

The two articles that were just discussed are the ones that are most relevant to the topic of this article, which is about the conversion from standard to minimal POS. Now that we have established that, let's get down to the meat of the matter, beginning with the following paragraph.

The minimal POS form has the shortest sum term (with the fewest literals) and gives the same information as the standard POS form.

Let's take a boolean expression in standard POS form and convert it into its equivalent boolean expression in minimal POS form.

Convert the boolean expression:

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

into minimal POS form. Here is the conversion:

= (A+B+C).(A+B+C')
= (A+B)+(CC')        [∵ AA' = 0]
= (A+B)              [∵ A+0 = A]

Therefore, the minimal POS form of:

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

is

(A+B)

Consider another example with three variables and three sum terms. Here is the expression:

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

Convert the above boolean expression into minimal POS form. Here is the conversion:

= (A+B+C).(A+B+C').(A+B'+C')
= ((A+B+C).(A+B+C')).((A+B+C').(A+B'+C'))
= (A+B+(CC')).(A+C'+(BB'))
= (A+B+0).(A+C'+0)
= (A+B).(A+C)

Therefore, the minimal POS form of the expression is:

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

is

(A+B).(A+C)

Another article, titled "the conversion of the standard sum of products to the minimal sum of products," is connected to this one and discusses a topic that is related to this one.

On the other hand, if you are reading each post in this article one at a time, then it is possible that you have already read this related post, which was the one that came before this one. That sums it up nicely. If you have any inquiries, please don't hesitate to get in touch with us by going to the "Contact Us" page that can be found at the very bottom of the article. Thank you and have a nice day.

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