Howtoimplementadesiredlogicfunction a 0 0 0 0 1 1 1 1

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Unformatted text preview: es to Logic Circuits Logic Gates • From switches • Truth Tables Logic Circuits • Identity Laws • From Truth Tables to Circuits (Sum of Products) Logic Circuit Minimization • Algebraic Manipulations • Truth Tables (Karnaugh Maps) Transistors (electronic switch) How to standardize minimizing logic circuits? How to implement a desired logic function? a 0 0 0 0 1 1 1 1 b 0 0 1 1 0 0 1 1 c out 00 11 00 11 00 11 00 10 How to implement a desired logic function? a 0 0 0 0 1 1 1 1 b 0 0 1 1 0 0 1 1 c out minterm 1) Write minterms 00 a b c 2) sum of products: 11 a b c • OR of all minterms where out=1 00 a b c 11 a b c 00 a b c 11 a b c 00 a b c 10 a b c How to implement a desired logic function? a 0 0 0 0 1 1 1 1 b 0 0 1 1 0 0 1 1 c out minterm 1) Write minterms 00 a b c 2) sum of products: 11 a b c • OR of all minterms where out=1 00 a b c out = abc + abc + abc 11 a b c 00 a b c 11 a b c 00 a b c 10 a b c corollary: any combinational circuit can be implemented in 1 lvls of logic (ignoring inverters) How does one find the most efficient equation? – Manipulate algebraically until…? – Use Karnaugh maps (optimize visually) – Use a software optimizer For large circuits – Decomposition & reuse of building blocks Sum of minterms yields a b c out 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 out = abc + abc + abc + abc Sum of minterms yields a c 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1...
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