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The Karnaugh map is therefore arranged in a 4 × 4 grid. The row and column indices (shown across the top and down the left side of the Karnaugh map) are ordered in Gray code rather than binary numerical order. Gray code ensures that only one variable changes between each pair of adjacent cells.
Those 16 numbers correspond to the minterms of Image:K-map minterms.svg used in a 4-variable [[:en:Karnaugh map File usage No pages on the English Wikipedia use this file (pages on other projects are not listed).
While this example was simplified by applying normal algebraic methods [= (′ +)], in less obvious cases a convenient method for finding minimal PoS/SoP forms of a function with up to four variables is using a Karnaugh map. The Quine–McCluskey algorithm can solve slightly larger problems.
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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.
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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)
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.