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Unformatted text preview: On Sets and Off Sets (Kmaps) 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 TwoLevel Simplification (Kmaps) 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 onset rows B's values change within the onset rows G = A B + A B = (A + A) B = B B's values stay the same within the onset rows A's values change within the onset rows B is eliminated, A remains A is eliminated, B remains Essence of Simplification: find two element subsets of the ONset 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 Kmap is an alternative method of representing the truth table that helps visualize adjacencies in up to 4 dimensions Beyond that, computerbased methods are needed 2variable Kmap 3variable Kmap 4variable Kmap 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 KMap...
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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.
 Winter '08
 WU

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