k-maps - 10/20/2009 Karnaugh Maps (K-maps) An excellent...

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10/20/2009 1 Karnaugh Maps (K-maps) An excellent tool for logic circuits minimization Karnaugh Maps Another representation of a truth table Excellent tool for implementing circuits from truth tables Used to find minimal SOP or POS expressions (combine adjacent 1-cells using combining theorem for SOP)
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10/20/2009 2 Karnaugh Maps Every cell is labeled logically adjacent to the one next to it (gray code) One bit changes at a time Useful in simulation and testing Normal: 0 00, 1 01, 2 10, 3 11. Gray code: 0 00, 1 01, 3 11, 2 10. Columns and rows are labeled with inputs, outputs are on inside of map Each cell corresponds to a minterm (or maxterm) 2-variable K-map A B Z (output) 0 0 m0 0 1 m1 1 0 m2 1 1 m3 A B 0 1 0 1 m0 m1 m2 m3
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3 3-variable K-map m0 m1 m2 m3 AB C 00 0 01 11 1 10 m4 m5 m6 m7 A B C Z 0 0 0 m0 0 0 1 m1 0 1 0 m2 0 1 1 m3 1 0 0 m4 1 0 1 m5 1 1 0 m6 1 1 1 m7 Notice Gray Code! Notice Swapped Columns! 4-variable K-map AB 00 01 11 10 CD 00 01 11 10 m0 m1 m3 m2 m4 m5 m7 m6 m12 m8 m13 m9 m15 m11 m14 m10 A B C D Z 0 0 0 0 m0 0 0 0 1 m1 0 0 1 0 m2 0 0 1 1 m3 0 1
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k-maps - 10/20/2009 Karnaugh Maps (K-maps) An excellent...

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