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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 the technique 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 ] or Marquand diagram . [ 4 ]
For the case when the Boolean function is specified by a circuit (that is, we want to find an equivalent circuit of minimum size possible), the unbounded circuit minimization problem was long-conjectured to be -complete in time complexity, a result finally proved in 2008, [4] but there are effective heuristics such as Karnaugh maps and the ...
"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) The history of Karnaugh's development of his "chart" or "map" method is obscure.
Boolean formulas can also be displayed as a graph: Propositional directed acyclic graph. Digital circuit diagram of logic gates, a Boolean circuit; And-inverter graph, using only AND and NOT; In order to optimize electronic circuits, Boolean formulas can be minimized using the Quine–McCluskey algorithm or Karnaugh map.
The Quine–McCluskey algorithm is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean F has been reached. It is sometimes referred to as the tabulation method.
Plotting zeroes of factors on a Veitch diagram or Karnaugh map is as easy as locating ones for a sum-of-products expression. […] To illustrate, using Dineley's example (A+BC)(A+C): […] The zeroes resulting from A+BC will be located wherever both A and BC are zero. Therefore we locate on the map the expression A * BC (which is equal to A * B ...
Karnaugh earned a B.A in physics from the City College of New York in 1948 and a PhD. in physics from Yale in 1952. [1]He later studied mathematics and physics at City College of New York (1944 to 1948) and transferred to Yale University to complete his B.Sc. (1949), M.Sc. (1950) and Ph.D. in physics with a thesis on The Theory of Magnetic Resonance and Lambda-Type Doubling in Nitric-Oxide (1952).
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.