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In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
In English, for example, run, runs, ran, and running are forms of the same lexeme, so we can select one of them; ex. run, to represent all the forms. Lexical databases such as Unitex use this kind of representation. Lemmatisation is the process of converting a word to its canonical form.
A logical formula is considered to be in DNF if it is a disjunction of one or more conjunctions of one or more literals. [2] [3] [4] A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every conjunction and each conjunction appears at most once (up to the order of variables).
In sum-of-products (SOP) form, AND gates form the smallest unit and are stitched together using ORs, whereas in product-of-sums (POS) form it is opposite. POS form requires parentheses to group the OR terms together under AND gates, because OR has lower precedence than AND. Both SOP and POS forms translate nicely into circuit logic.
A canonical form thus provides a classification theorem and more, in that it not only classifies every class, but also gives a distinguished (canonical) representative for each object in the class. Formally, a canonicalization with respect to an equivalence relation R on a set S is a mapping c : S → S such that for all s , s 1 , s 2 ∈ S :
Text normalization is frequently used when converting text to speech. Numbers, dates, acronyms, and abbreviations are non-standard "words" that need to be pronounced differently depending on context. [2] For example: "$200" would be pronounced as "two hundred dollars" in English, but as "lua selau tālā" in Samoan. [3]
The POS expression gives a complement of the function (if F is the function so its complement will be F'). [10] Karnaugh maps can also be used to simplify logic expressions in software design. Boolean conditions, as used for example in conditional statements, can get very complicated, which makes the code difficult to read and to maintain. Once ...
Sop at Christmas, Sweden, 1910. A sop is a piece of bread or toast that is drenched in liquid and then eaten. In medieval cuisine, sops were very common; they were served with broth, soup, or wine and then picked apart into smaller pieces to soak in the liquid. At elaborate feasts, bread was often pre-cut into finger-sized pieces rather than ...