Representation of Boolean functions in Canonical and Standard Forms:

Minterm or a standard product: Minterms are standard product terms obtained by AND operations on ‘n’ variables under discussion.

Suppose n = 2 (x and y) and, we know ‘0’ represents complements i.e. x’ and y’

so, we have x, y, x’ and y’. Therefore, Minterms combinations are shown in table below.

Minterms

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Maxterm or standard sum: Maxterms are standard sum terms obtained by OR operation of ‘n’ variables and their complements.

Suppose n = 2 (x and y)

and, we know ‘0’ represents complements i.e. x’ and y’

so, we have x, y, x’ and y’

Generally, Maxterms are represented as complements of Minterms.

We tabulate Maxterm combinations in table below.

Maxterms

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Now lets study two more concepts to use minterms and maxterms.

SOM (Sum of Minterms) is an equivalent statement of Sum of Standard products. This topic is elaborated further here.
POM (Product of Maxterms) is simply obtained by taking the complement of sum of Minterms. Thid topic is elaborated further here.

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