# karnaugh maps (5 & 6 variables)

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Karnaugh Maps (5 & 6 variables)

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• The format of a 5-variable k-map is two 4-variable k-maps side by side.

• The most significant bit A is used to select which of the 4–variable k-map is being used.

• The BCDE bits are used to select the entry in the 4-variable k-map.

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• The numbering of the squares corresponds to the decimal equivalent of the minterm that is associated with the square.

• Notice how some of the rows and columns are swapped from a natural ordering to keep adjacent squares differ in the sense of only one variable.

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4

• The adjacent squares in each individual

4-variavle k-map remain. In addition, adjacent

squares can span across the two 4-variable k-

maps.

• These two 4-variable k-maps can be imagine as being stacked on top of each other. The squares that are lying on top of each other are also adjacent in the two k-maps.

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• Ones in the k-map have to be grouped in powers of two. So for the 5-variable k-map, the largest group will be 32.

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• Examples on Selecting two cells from two k-maps.

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• Examples on Selecting four cells from two k-maps.

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• Examples on Selecting eight cells from two k-maps.

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• Examples on Selecting sixteen cells from two k-maps.

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• Example on Selecting thirty two cells from two k-maps.

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Questions

Q1: F = Σ (1, 3, 4, 5, 11, 12, 14, 16, 20, 21, 30)

Q2: F = Σ (0, 2, 3, 5, 7, 8, 11, 13, 17, 19, 23, 24, 29, 30)

Q3: F = Σ (0, 1, 2, 3, 8, 9, 16, 17, 20, 21, 24, 25, 28, 29, 30, 31)

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Karnaugh Maps (6 variables)

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• The format of a 6-variable k-map is four 4-variable k-maps.

• Adjacent ones in the k-maps can be grouped together in power of 2 up to 64.

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Questions

Q1: F = Σ (1, 3, 4, 5, 11, 12, 14, 16, 20, 21, 30)

Q2: F = Σ (0, 2, 3, 5, 7, 8, 11, 13, 17, 19, 23, 24, 29, 30)

Q3: F = Σ (0, 1, 2, 3, 8, 9, 16, 17, 20, 21, 24, 25, 28, 29, 30, 31)

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Questions

Q1: F = Σ (0, 2, 4, 8, 10, 13, 15, 16, 18, 20, 23, 24, 26, 32, 34, 40, 41, 42, 45, 47, 48, 50, 56, 57, 58, 60, 61)

Q2: F = Σ (0, 1, 2, 3, 4, 5, 8, 9, 12, 13, 16, 17, 18, 19, 24, 25, 36, 37, 38, 39, 52, 53, 60, 61)

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