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digital

  1. 1. MINTERMS AND MAXTERMS A binary variable may appear either in its normalform x or in its complement form x . Let us consider twobinary variables x and y, connected with AND operator.There are four possible combinations: xy, xy,xy and xy.These four possible combinations of input variables x andy can be represented on a venn diagram. A minterm isthe product of all the variables within the logic system,complemented or not. Thus, if x and y are the variables,the following are athe minterms: xy, A venn diagram consistsof a rectangle, inside whichthere are two overlapping circles, one for each variable xand y. Such a venn diagram for two variables is shownin this shows all the domains of the four possiblecombinations of the input variables x and y. Venn diagrams may be used to explain the laws ofBoolean algebra. Venn diagrams may be used to
  2. 2. explain the laws of Boolean algebra. X=xy+x=xy+xy’. Venn diagram for two variables x=xy+x. A maxterm is of all the variables within the logicsystem, complemented or not. If x,y and z are all thevariables within a system, the following are themaxterms. x+y+z x+y+z’ x+y’+z x+y’+z’ x’+y+z x’+y+z’ x’+y’+z x’+y’+z’
  3. 3. Boolean functions expressed either as a sum ofminterms or as product of maxterms are said to be incanonical form.

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