karnaugh map
a karnaugh map is a modified form of truth table in which the arrangement of combinations is particularly convenient. each 
-variable map consists of 
cells (squares), representing all possible combinations of these variables.
the function value associated with a particular combination is entered in the corresponding cell. for example, the map of the function
is shown in ex-kmap-1, where the value 1 is entered in cells 2, 6, and 7 (see fig-kmap-3vars). a blank cell means that for the corresponding combination, the value of the function is 0. the minterm that corresponds to a particular cell is determined as in the truth table. the variable 
appears in uncomplemented form in the product if it has value 1 in the corresponding cell, and in complemented form if it has value 0. for example, cell 6 in the three-variable map corresponds to 
, and in the four-variable map it corresponds to 
. ex-kmap-2 shows the map for function 
.
[cite:@kohavi_switching_2010 chapter 4.2 the map method]
-variable map consists of cells (squares), representing all possible combinations of these variables.the function value associated with a particular combination is entered in the corresponding cell. for example, the map of the function
is shown in ex-kmap-1, where the value 1 is entered in cells 2, 6, and 7 (see fig-kmap-3vars). a blank cell means that for the corresponding combination, the value of the function is 0. the minterm that corresponds to a particular cell is determined as in the truth table. the variable appears in uncomplemented form in the product if it has value 1 in the corresponding cell, and in complemented form if it has value 0. for example, cell 6 in the three-variable map corresponds to , and in the four-variable map it corresponds to . ex-kmap-2 shows the map for function .[cite:@kohavi_switching_2010 chapter 4.2 the map method]
 |  |  |  |  |  |  |  | |
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
| 2 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 3 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 |
| 4 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
| 5 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |
| 6 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| 7 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
| 8 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
| 9 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
[cite:@kohavi_switching_2010 chapter 4.2 the map method]