standard forms
Summary
Canonical form
- canonical sum-of-products -> sum-of-minterms
- canonical product-of-sums -> product-of-maxterms
Concept
Standard forms for boolean expressions
| Form | Definition | Example |
|---|---|---|
| Literal | boolean variable or its complement | |
| Product Term | literal logical product of literals | |
| Sum Term | literal 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
2ⁿminterms and2ⁿmaxterms overnvariables, they represent all the rows of the truth table
Application
Identifying SOP and POS
Sum-of-minterms
0is the complement
Product-of-maxterms
1is the complement