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# week3a - On Sets and Off Sets(K-maps X 0 0 0 0 1 1 1 1 Y 0...

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1 On Sets and Off Sets (K-maps) 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

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2 Two-Level Simplification (K-maps) 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!
3 BC CD AB  00  01  11  10  00  01  11  10  00  01  11  10  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 Numbering Scheme: 00, 01, 11, 10

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week3a - On Sets and Off Sets(K-maps X 0 0 0 0 1 1 1 1 Y 0...

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