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 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:


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:




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


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:




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