What is variable - Definition and Meaning - Math Dictionary | math variable[/caption]
math variable
A Boolean action is declared by an algebraic announcement consisting of bifold variables, the constants 0 and 1, and the argumentation operation symbols For a accustomed set of ethics of the bifold variables involved, the boolean action can accept a amount of 0 or 1. For example, the boolean action is authentic in agreement of three bifold variables . The action is according to 1 if and accompanying or .Every boolean action can be bidding by an algebraic expression, such as one mentioned above, or in agreement of a Accuracy Table. A action may be bidding through several algebraic expressions, on annual of them actuality logically equivalent, but there is alone one different accuracy table for every function.A Boolean action can be adapted from an algebraic announcement into a ambit diagram composed of argumentation gates affiliated in a accurate structure. Ambit diagram for –
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Variable in Math and Statistics | math variable[/caption]
Canonical and Accepted Forms –Any bifold capricious can booty one of two forms, or . A boolean action can be bidding in agreement of bifold variables. If all the bifold variables are accumulated calm application the AND operation, again there are a absolute of combinations back anniversary capricious can booty two forms.Each of the combinations is alleged a minterm or accepted product. A minterm is represented by area is the decimal agnate of the bifold cardinal the minterm is designated.Important Note – In a minterm, the bifold capricious is un-primed if the capricious is 1 and it is abreast if the capricious is 0 i.e. if the minterm is again that agency and .For example, for a boolean action in two variables the minterms are –
In a agnate way, if the variables are accumulated calm with OR operation, again the appellation acquired is alleged a maxterm or accepted sum. A maxterm is represented by area is the decimal agnate of the bifold cardinal the maxterm is designated.
Important Note – In a maxterm, the bifold capricious is un-primed if the capricious is 0 and it is abreast if the capricious is 1 i.e. if the minterm is again that agency and .For example, for a boolean action in two variables the minterms are –
Minterms and Maxterms for action in 3 variables –
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Variables - YouTube | math variable[/caption]
Relation amid Minterms and Maxterms – Anniversary minterm is the accompaniment of it’s agnate maxterm.For example, for a boolean action in two variables –
Constructing Boolean Functions – Now that we apperceive what minterms and maxterms are, we can use them to assemble boolean expressions.
“A Boolean action can be bidding algebraically from a accustomed accuracy table by basal a minterm for anniversary aggregate of the variables that produces a 1 in the action and again demography the OR of all those terms.”
For example, accede two functions and with the afterward accuracy tables –The action is 1 for the afterward combinations of – 001,100,111The agnate minterms are- , , .Therefore the algebraic announcement for is-Similary, the algebraic announcement for is-If we use De Morgans Law on and all 1’s become 0 and all 0’s become 1. Therefore we get-On application De Morgans Law again-andWe can achieve from the aloft that boolean functions can be bidding as a sum of minterms or a artefact of maxterms.
“Boolean functions bidding as a sum of minterms or artefact of maxterms are said to be in approved form.
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Algebra Lesson for Kids: Facts | math variable[/caption]
Standard Forms –Canonical forms are basal forms acquired from the accuracy table of the function. These forms are usually not acclimated to represent the action as they are bulky to address and it is bigger to represent the action in the atomic cardinal of literals possible.There are two types of accepted forms –
Note – The aloft expressions are not equivalent, they are aloof examples.
GATE CS Corner Questions
Practicing the afterward questions will advice you analysis your knowledge. All questions accept been asked in GATE in antecedent years or in GATE Mock Tests. It is awful recommended that you convenance them.
1. GATE CS 2010, Question 61. GATE CS 2008, Question 71. GATE CS 2014 Set-1, Question 17
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Math Expressions | MathCaptain.com | math variable[/caption]
References-
Digital Design 5th Edition, by Morris Mano and Michael Ciletti
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