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?"

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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.

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