Product of Sum

Product of Sum abbreviated for POS.

The product of Sum form is a form in which products of different sum terms of inputs are taken. These are not arithmetic product and sum but they are logical Boolean AND and OR respectively.

To better understand about Product of Sum, we need to know about Max term.

Max Term

Maxterm means the term or expression that is true for a maximum number of input combinations or that is false for only one combination of inputs.

Since OR gate also gives false for only one input combination. So Maxterm is OR of either complemented or non-complemented inputs.

Max terms for 3 input variables are given below.

3 inputs have 8 different combinations so it will have 8 maxterms. Maxterms are denoted by capital M and decimal combination number In the subscript as shown in the table given above.

In maxterm, each input is complemented because Maxterm gives ‘0’ only when the mentioned combination is applied and Maxterm is complement of minterm.

M₃               =             m̅₃

M₃               =             (A̅BC)’

M₃               =             A + B̅ +C̅               DE Morgan’s law

Which is why for A=0 Max term consist A & for A=1 Max term consist A̅.