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A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced it in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] (aka.
In the early days, logic design involved manipulating the truth table representations as Karnaugh maps. The Karnaugh map-based minimization of logic is guided by a set of rules on how entries in the maps can be combined. A human designer can typically only work with Karnaugh maps containing up to four to six variables.
Two-dimensional Gray codes also have uses in location identifications schemes, where the code would be applied to area maps such as a Mercator projection of the earth's surface and an appropriate cyclic two-dimensional distance function such as the Mannheim metric be used to calculate the distance between two encoded locations, thereby ...
In Chapter 6, section 6.4 "Karnaugh map representation of Boolean functions" they begin with: "The Karnaugh map 1 [1 Karnaugh 1953] is one of the most powerful tools in the repertory of the logic designer. ... A Karnaugh map may be regarded either as a pictorial form of a truth table or as an extension of the Venn diagram." [13] (pp 103–104)
Don't-care terms are important to consider in minimizing logic circuit design, including graphical methods like Karnaugh–Veitch maps and algebraic methods such as the Quine–McCluskey algorithm. In 1958, Seymour Ginsburg proved that minimization of states of a finite-state machine with don't-care conditions does not necessarily yield a ...
The primary difference between the Veitch and Karnaugh versions is that the Veitch diagram presents the data in the binary sequence used in the truth table while the Karnaugh map interchanges the third and fourth rows and the third and fourth columns. The general digital computer community chose the Karnaugh approach.
Now we know roughly how the hazard is occurring, for a clearer picture and the solution on how to solve this problem, we would look to the Karnaugh map. The two gates are shown by solid rings, and the hazard can be seen under the dashed ring. A theorem proved by Huffman [2] tells us that by adding a redundant loop 'BC' this will eliminate the ...
Example: The map method usually is done by inspection. The following example expands the algebraic method to show the "trick" behind the combining of terms on a Karnaugh map: Minterms #3 and #7 abut, #7 and #6 abut, and #4 and #6 abut (because the table's edges wrap around). So each of these pairs can be reduced.