Discussion
In a Karnaugh map, adjacent cells are arranged so that they differ by
Answer: C
Correct answer: one variable
Adjacent cells in a Karnaugh map differ in exactly one variable, and that single property is what makes the map work. When two adjacent cells both contain 1, the variable that differs between them can be eliminated. Algebraically this is the identity \[ A B + A \bar{B} = A(B + \bar{B}) = A. \] Combining a pair removes one variable, a group of four removes two, a group of eight removes three. The arrangement is achieved by labelling the axes in Gray code, in which successive values change one bit at a time: 00, 01, 11, 10. Plain binary order would place 01 next to 10, which differ in two bits, and the grouping would be invalid. The map also wraps round, so the first and last columns are adjacent, and in a four-variable map the four corner cells form a valid group of four. Missing that wraparound is the commonest error in using the method.
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