standard forms

Complete

Summary

Canonical form

  • canonical sum-of-products -> sum-of-minterms
  • canonical product-of-sums -> product-of-maxterms

Concept

Standard forms for boolean expressions

FormDefinitionExample
Literalboolean variable or its complement,
Product Termliteral
logical product of literals		,
Sum Termliteral
logical sum of literals		,
Sum-of-Products(SOP)product term
logical sum of product terms		, , ,
Product-of-Sums(POS)sum term
logical product of sum terms		, , ,

related to CNF

Minterms and maxterms

  • minterm
    • product term
    • -> 0, -> 1
  • maxterm
    • sum term
    • complement of minterm
    • -> 1, -> 0

2ⁿ minterms and 2ⁿ maxterms over n variables, they represent all the rows of the truth table

Application

Identifying SOP and POS

Sum-of-minterms

0 is the complement

Product-of-maxterms

1 is the complement