Electrical and Computer Engineering 2277A/B Lecture Notes - Lecture 11: Maurice Karnaugh, Distributive Property, Gray Code
2 Jan 2021
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Graphical method for minimizing boolean functions into standard sum of products or standard product of sums form. Minimized standard-form expression = minimum number of terms with minimum number of literals in each term. Two-level* circuit with minimum number of gates and minimum number of inputs to each gate. *not counting any not gates to invert input terms. Cells contain the logic levels of their minterms. Construct k-map with 1 in each cell corresponding to minterms for which f = 1; leave other cells blank. Circle pairs of horizontally or vertically adjacent cells containing 1s. For each circled pair of cells, write a product term consisting of the variables that have the same value for both cells. Write a sum of products expression combining the terms obtained in step 3. Draw circuit schematic based on minimized expression from step 4. Circling pairs of terms is equivalent to simplifying a canonical sum of minterms using the distributive property:
