Logic Circuit Minimization Using Karnaugh Map Lookup Tables
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|John Eric Franklin|
|Four variable truth tables drawn in a four by four grid is called a Karnaugh map to an electrical engineer. Karnaugh maps were developed in the 1950's and help to produce sum-of-product equations (AND,OR). I have added the XOR operator (exclusive-or) in order to produce shorter equations. The equations are probably the shortest boolean equations possible for these truth tables. They were generated by a computer program that started with the simplest truth tables; one half true, one half false (the variables A,B,C,and D) and connected them together to form all 2^16 (65536) combinations of four variable truth tables. The boolean equations are in prefix notation. Note the interesting order of columns and rows in a Karnaugh map (0,1,3,2) or (00,01,11,10 in binary). This order is so any two touching squares differ in only one digit in binary.|
|Math Topics:||Logic/Foundations, Engineering|
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