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l9_15_6

# l9_15_6 - Multi-Level Logic Advantages Reduced sum of...

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1 ECE 15A Fundamentals of Logic Design Lecture 9 Malgorzata Marek-Sadowska Electrical and Computer Engineering Department UCSB 2 Multi-Level Logic: Advantages Reduced sum of products form: x = A D F + A E F + B D F + B E F + C D F + C E F + G 6 x 3-input AND gates + 1 x 7-input OR gate (may not exist!) 25 wires (19 literals plus 6 internal wires) Factored form: = (A + B + C) (D + E) F + G 1 x 3-input OR gate, 2 x 2-input OR gates, 1 x 3-input AND gate 10 wires (7 literals plus 3 internal wires) 1 2 3 4 5 6 7 A A B B C C D D D E E E F F F F F F G x 1 2 3 4 A B C D E F G x 3 Multi-Level Logic: CAD Tools for Simplification Multi-Level Optimization: 1. Factor out common sublogic (reduce fan-in, increase gate levels), subject to timing constraints 2. Map factored form onto library of gates 3. Minimize number of literals (correlates with number of wires) 4 Multi-Level Logic: CAD Tools for Simplification Factoring: expression in two level form re-expressed in multi-level form F = A C + A D + B C + B D + E can be rewritten as: F = (A + B) (C + D) + E (9 literals & 5 gates) (7 literals & 4 gates) Before Factoring After Factoring A A A B B B C C C D D D E E F F 5 Multi-Level Logic: CAD Tools for Simplification Decomposition: Take a single Boolean expression and replace with collection of new expressions: F = A B C + A B D + A' C' D' + B' C' D' F rewritten as: F = X Y + X' Y' X = A B Y = C + D (12 literals) (8 literals) Before Decomposition After Decomposition F A B C D F A A A B B B C C C D D

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l9_15_6 - Multi-Level Logic Advantages Reduced sum of...

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