3. IndexThe map methodRules for mapPresent technique.Types of variablesUses of k-mapApplication of k-map.
4. WHAT IS K-MAP?The pictorial representation of variablesfrom which the Boolean expression ortruth table can be identified.It avoids ambiguity during logic designing.Since there is number of probability inmapping the answer would be same andavoid confusion.It is denoted as k-map since it is found bythe person karnaugh.
5. THE MAPStraight procedure for minimizing BooleanfunctionsConsidered as pictorial form of a truthtableIt is a diagram made of squaresIt consists of minterms[0] & maxterms[1]In Some cases don’t care conditions areused [represented by ‘x’] .
6. RulesMapping can be done horizontally orvertically but not in diagonally.Wrapping technique can be done onlyform three variable map.Only the maxterms can be mapped to forma Boolean expression.Overlapping of maxterms is possible,utmost once.
7. present techniqueMaxterms are grouped together to derivethe expression.Don’t care conditions alone cannot bemapped to form a group.The mapping can be selected dependingon the variable usedCorresponding variables should be writtenfor the mapped values.The grouping is done in even numbers.
8. Basic’sThe frequently used variable mappings areTwo variable mapThree variable mapFour variable mapFive variable mapLet’s see this in detail
9. Two variable-mapFour minterms for twovariablesIt consists of four squares YThe 0 and 1 marked in Xrow and columndesignate the values of 0 0variablesA two variable is shownAnd the expression forthe group is 1 1=X+Y
10. Three variable mapIt consists of eight minterms for threebinary variablesIt has eight squaresMinterms are not arranged in binarysequence but similar to gray codeWrapping technique can start using onlyfrom the three variable mappingConsider the following truth table for whichthe mapping can be done.
11. Truth tableD.NO A B C S C 0 0 0 0 0 0 1 0 0 1 1 0 2 0 1 0 1 0 3 0 1 1 0 1 4 1 0 0 1 0 5 1 0 1 0 1 6 1 1 0 0 1 7 1 1 1 1 1
12. Representation of three variable map YZ 00 01 11 10X m0 m1 m3 M2 0 m4 m5 m7 m6 1
13. FOUR VARIABLE MAPIn this method four variables are used.The map contains 16 squares.Grouping can be done only for themaxtermsWrapping can be done by folding the map.Adjacent groups cannot be formed since itcontains single map.The representation of four variable map is.
14. Four variable map C CD AB 00 01 10 11 Adjacent 1 1 1 groups 00 can’t be formed 01 1 B 10A Wrapping can be 11 1 1 1 cone
15. Five variable mapIt consists of five variables (A,B,C,D,E)Left hand four variable consists of 16 squaresand right consists of 16 squaresActually it is the combination of two four variablemapThe left table represents the variable value A=0and right table represents the A value as ‘1’.Adjacent group in the tables can be representedonceConsider the following truth table for which themapping is done.
16. Five variable map A=0 A=1 D D DEBC 0 2 2 3 16 17 19 18 4 5 7 6 20 21 23 22 C C 12 13 15 14 28 29 31 30B B 8 9 11 10 24 25 27 26
17. Representation of five variable map without using two four variable map Adjacent groups can’t be ABC 000 001 010 011 110 111 100 101 formed DE but it 00 0 1 2 3 6 7 4 5 gives the same 01 8 9 10 11 14 15 12 13 answer 24 25 26 27 30 31 28 29 10 11 16 17 18 19 22 23 20 21
18. DON’T CARE CONDITIONS Y CD 00 01 11 11 AB 00 x 1 1 X 01 0 x 1 0 X 10 0 0 1 0 W 11 0 0 1 0
19. DON’T CARE CONDITIONThe ‘x’ represents the position of don’t careconditions.The value of ‘x’ may 1 or 0 it depends ongrouping.The expression for the previous k-map is:A=c +a +bd +bd.Note that all the don’t care cannot be mapped asa single group.
20. OUR METHODCheck the maxterms in the truth tableitself.Write the corresponding expression.Simplify the expression with the help ofDEMORGAN’S theory.The is no need of k-map in this method.
21. usesK-map is used to derive any form of logicalcircuitIt is used in design and analysis procedureIt is used in Quine-McCluskey methodSimplification of Boolean expression iseasierIt is used in sum of product and in productof sum method.
22. ApplicationThe k-map can be used in combinationalcircuit and in sequential circuit.Full adder and half adder can be easilyanalyzed with the help of k-map.It is used in the in tabular method tosimplify the Boolean expression evensimpler than that.
23. conclusionThus k-map is a major topic in electronicsIt is used in simplification of Booleanexpression & logic gatesIt is used in the conversion of truth table toBoolean expression and vice versa.It is better to use a k-map than the tabularmethod.
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