03_kmaps - On Sets and Off Sets X 0 0 0 0 1 1 1 1 Y 0 0 1 1...

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55 On Sets and Off Sets Readings: 4-4.4 On Set is the set of input patterns where the function is TRUE Off Set is the set of input patterns where the function is FALSE XY Z H 0000 0011 0100 0111 1001 1011 1100 1110 56 A 0 0 1 1 B 0 1 0 1 G 1 0 1 0 0 0 1 1 B 0 1 0 1 F 0 0 1 1 Two-Level Simplification Key Tool: The Uniting Theorem — A (B + B) = A F = A B + A B = A (B + B) = A A's values don't change within the on-set rows B's values change within the on-set rows G = A B + A B = (A + A) B = B B's values stay the same within the on-set rows A's values change within the on-set rows B is eliminated, A remains A is eliminated, B remains Essence of Simplification: find two element subsets of the ON-set where only one variable changes its value. This single varying variable can be eliminated!
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57 AB CD A C B D Karnaugh Maps Karnaugh Map Method K-map is an alternative method of representing the truth table that helps visualize adjacencies in up to 4 dimensions Beyond that, computer-based methods are needed 2-variable K-map 3-variable K-map 4-variable K-map B B AB C B C 58 Truth Tables to K-Maps AB CD C B D B B AB C B C F 0 0 0 0 1 0 1 0 1 1 1 0 A B C G 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 A B C H 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0
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03_kmaps - On Sets and Off Sets X 0 0 0 0 1 1 1 1 Y 0 0 1 1...

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