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The Map Method

The Map method, also known as Karnaugh maps (K-Maps), provides an efficient way to simplify Boolean functions. Using Karnaugh maps, designers can visually group minterms, minimizing the expression to a manageable number of terms. For two-variable and three-variable maps, adjacent cells represent minterms differing by only one variable, aiding in simplification. This method extends to four-variable maps and multilevel NAND/NOR circuit conversions, facilitating design by converting AND-OR configurations into NAND/NOR formats while ensuring proper handling of bubbles.

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The Map Method

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  1. The Map Method Truth table of fn is unique but fn can be in many different algebraic forms Simplification by using boolean algebra is often difficult because we don’t know how to proceed Map method or Karnaugh map (K_Map) is simple and straightforward method that produces minimum number of terms.

  2. Two-Variable Map A fn variable have 2n minterms (cells)

  3. Three- Variable Map • Adjacent cells represent minterms that differs by only one variable. Therefore, adjacent cells are identical except for one variable that appears complemented in one cell and uncomplemented in the adjacent cell. • Example : F(x,y,x) = ∑ (2,3,4,5)

  4. Another example : F(x,y,z) = ∑(3,4,6,7)

  5. Four variable Map

  6. Multilevel NAND circuits To convert multilevel AND-OR to all NAND: • Convert all ANDs with AND-invert • Convert all ORs with invert-OR • Check the bubbles in diagrams if any of them is not compensated by another small circle along the same line insert an inverter(One input NAND) or complement the input literal

  7. Implementing NOR circuits To convert multilevel AND-OR to all NOR: • Convert all ORs with invert-OR • Convert all ANDs with invert-AND • Check the bubbles in diagrams if any of them is not compensated by another small circle along the same line insert an inverter(One input NOR) or complement the input literal

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