CH5 - Karnaugh Maps Hasan Zidan Department of Electrical...

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arnaugh aps Karnaugh Maps Hasan Zidan epartment of Electrical Engineering Department of Electrical Engineering AUST 1
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Karnaugh Map Minimization Karnaugh Map (or K-map) minimization is a visual minimization technique It is an application of adjacency theorem Guarantees a minimal expression Easy and Fast b l i l d Problems include: Applicable to limited number of variables (4 ~ 6) Errors in translation from Truth Table to K-map Errors in reading final expression z Basic K-map is a 2-D rectangular array of cells z Arrangement of cells in array facilitates recognition of adjacent terms djacent terms differ in one variable value; difference of one bit 2 z Adjacent terms differ in one variable value; difference of one bit of input row values e.g. m6 (110), m7 (111)
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K-Maps K ap has a square for each ‘ or‘ of a boolean function A K-map has a square for each ‘1’ or ‘0’ of a boolean function. One variable K-map has 2 1 = 2 squares. wo variable K ap has 2 = uares Two variable K-map has 2 4 squares Three variable K-map has 2 3 = 8 squares Four variable K-map has 2 4 = 16 squares 1 variable 3 variable 4 ariable 2 variable vb e 3
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K-map Minimization (cont.) For any cell in 2-D array, there are four direct neighbors (top, bottom, left, right) array show adjacencies of up to four variables 2-D array show adjacencies of up to four variables. AB 00 01 11 10 CD A 00 01 AB 01 11 10 C 00 11 C D 0 C 1 10 B B our variable K ap 4 Four variable K-map Three variable K-map
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Truth Table to K-map Number of TT rows MUST match number of K-map cells AB 00 0 1 1 1 1 0 00 CD A 0 0 0 0 0 0 0 0 1 x x x 0 1 0 A B C D F 2 0 1 D 0 0 0 0 0 1 1 1 1 0 0 1 x x x x 1 0 1 0 m13 m12 m5 m9 m0 m1 1 1 1 0 C 0 1 1 1 1 0 0 0 1 0 0 1 x x x x 1 0 1 0 m15 m7 m3 B 1 1 1 1 0 1 1 1 1 0 0 1 x x x x 1 0 1 0 5 111 x 1
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K-map Minimization ntryofTTdataintoK ap Entry of TT data into K-map 0 0 0 0 0 A B C D F AB 00 01 11 10 CD A 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 00 01 0 0 0 1 1 1 0 0 041 28 1 2 3 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 C D 1 00 0 1 3 5 7 13 15 9 4 5 6 7 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 10 B 1 0 0 0 2 6 14 10 8 9 10 Watch out for ordering of 10 and 11 rows and columns!
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CH5 - Karnaugh Maps Hasan Zidan Department of Electrical...

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