week3a - On Sets and Off Sets (K-maps) On Set is the set of...

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Unformatted text preview: 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 A 0 0 1 1 B 0 1 0 1 G 1 0 1 0 A 0 0 1 1 B 0 1 0 1 F 0 0 1 1 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! B A 0 1 0 1 BC A B C CD AB C 00 01 11 10 0 1 00 01 11 10 00 01 11 10 A D B 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 Gray Code only a single bit changes from code word to next code word 00 10 01 11 000 001 011 010 100 101 111 110 0000 0001 0011 0010 0100 0101 0111 0110 K-Map...
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This note was uploaded on 04/07/2008 for the course EECS 203 taught by Professor Wu during the Winter '08 term at Northwestern.

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week3a - On Sets and Off Sets (K-maps) On Set is the set of...

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