How to Find Product Of Sums or POS from Truth Table ?

Product Of Sum or POS Form

POS stands for Product of Sum and totally opposite to SOP form . When an expression is expressed in a product of binary terms ( A term refers to a set of binary variables, where each binary variable is combined with an operation) called Maxterms than it is said to be Product of Sum.

In other words, An expression consisting only Maxterms is called Product of Sum. For  example, (A+B)(A’+B) is a POS expression.
[other concept Minterms, A.B+A’B’]

POS can be categorized in two forms :

– Canonical or Standard POS form: In this, each and every binary variable must have in each term. For example :- (A+B).(A’+B).

– Minimal POS form: In this, the standard POS expression is reduced up in the minimum possible expression.

A Question can be asked in three ways:-

1) In the form Truth table
2) In the form of non-canonical Expression
3) In the of form of Boolean function

For the given table, simplify it in POS expression

Or

Find POS from Truth Table

Points to Remember :

• Always consider low output (0)
• In Product of Sum or POS, every term in the expression is refereed to Maxterm
• A Maxterm is represented as M(Capital M)
• Consider A’ =1, A=0

Step 1. Since there are 2 variables , so therefore there would be 2ⁿ combinations which is 2² =4.
We consider a low output as Maxterm . a Maxterm is denoted as M.
Y= M₀+M₁
Y = (A+B).(A+B’)                           :- It is in Canonical POS form

In Product of Sum each term is combined with AND operation and within each term, every variable combined with OR operation.

Step 2. Now narrow the founded expression down to minimal Product of Sume or POS form. In this, you should know rules of Boolean expression or K-map

Y= A+BB’                         :-  x+yz = (x+y)(x+z)
Y= A + 0                            :- x.x’ =0
Y= A

OR

Considering, A= 0, A’=1

Y= A

A is your answer.