A.Abhari CPS2131 Chapter 3: Gate-Level Minimization Topics in this Chapter: The Map Method...
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Transcript of A.Abhari CPS2131 Chapter 3: Gate-Level Minimization Topics in this Chapter: The Map Method...
![Page 1: A.Abhari CPS2131 Chapter 3: Gate-Level Minimization Topics in this Chapter: The Map Method Two-Variable Map Three- Variable Map Four/Five variable Map.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f265503460f94c3cf72/html5/thumbnails/1.jpg)
A.Abhari CPS213 1
Chapter 3: Gate-Level Minimization
Topics in this Chapter:
• The Map Method• Two-Variable Map• Three- Variable Map• Four/Five variable Map• Don’t –Care Conditions• Product of Sums Simplification • Implementing NAND and NOR circuits
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A.Abhari CPS213 2
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.
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A.Abhari CPS213 3
Two-Variable Map
A fn variable have 2n minterms (cells)
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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,z) = ∑ (2,3,4,5)
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Another example : F(x,y,z) = ∑(3,4,6,7)
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Four variable Map
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Multilevel NAND circuits
To convert multilevel AND-OR to all NAND:
1. Convert all ANDs with AND-invert
2. Convert all ORs with invert-OR
3. Check the bubbles in diagrams if any of them is not compensated by another small circle along the same line insert an inverter (it is one input NAND gate) or complement the input literal
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Implementing NOR circuits
To convert multilevel AND-OR to all NOR:
1. Convert all ORs with OR-invert
2. Convert all ANDs with invert-AND
3. 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 gate) or complement the input literal
![Page 29: A.Abhari CPS2131 Chapter 3: Gate-Level Minimization Topics in this Chapter: The Map Method Two-Variable Map Three- Variable Map Four/Five variable Map.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f265503460f94c3cf72/html5/thumbnails/29.jpg)
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