Boolean algebra is the mathematics used to analyze digital gates and circuits.
Boolean Algebra is made up of the Boolean laws. Maxterm & Minterm are very important topics of Boolean algebra.
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Minterm is a product of all the literals (in either complement or without complement form).
if we have two boolean variables X and Y
then X.(~Y) is a minterm. we can express complement ~Y as Y’
so, the above minterm can be expressed as XY’
So, if we have two variables then the minterm will consists of product of both the variables
Maxterm is a sum of all the literals (with or without complement).
if we have two boolean variables X and Y then X+(Y’) is a maxterm. we can express complement ~Y as Y’ so, the above maxterm can be expressed as X + Y’ So, if we have two variables then the maxterm will consists of sum of both the variables.
if we have two variables X and Y then,
Following is a canonical expression consisting of minterms XY + X’Y’ (Canonical Sum of products-SOP) and
Following is a canonical expression consisting of maxterm (X+Y) . (X’ + Y’) (Canonical product of Sum POS)
Different forms of Expressions
There are two forms of expression.
Sum of Products (SOP) ¢This type of expression is formed by adding the product. For example if A and B are two boolean variables. Then A’B+B is an SOP ¢In this each term might not have all the variables.
Product of Sums (POS) ¢This type of expression is formed by multiplying the sum. For example if A and B are two boolean variables. Then (A’+B). B is an SOP ¢In this each term might not have all the variables.
Key Differenece between SOP and POS
•SOP (Sum of product) generates expression in which all the variables in a domain are first multiplied then added. On the contrary, the POS (Product of Sum) represents the Boolean expression having variables summed then multiplied with each other.
•Minterms or product terms are mainly used in the SOP which associates with the high (1) value. Conversely, in POS, Maxterms or sum terms are employed, which produces a low (0) value.
•In the SOP, method, the value ‘1’ is replaced by the variable and ‘0’ by its complement. In contrast, when it comes to POS a ‘0’ is substituted by the variable and ‘1’ by its complement.
•At last, all the terms are added with each other in case of SOP. As against, in POS, the terms are multiplied with each other in the last step of the process.