270L19-Two+Level+Logic+Minimization

270L19-Two+Level+Logic+Minimization - Logic Synthesis: From...

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1 UM EECS 270 Fall 2009 Logic Synthesis: From Specs to Circuits • Implementation Styles – Random – Regular • Optimization Criteria – Area (roughly number of transistors) – Delay (roughly number of gates on longest circuit path) – Testability – Power consumption • 2-Level Synthesis – Classical (Exact) – Heuristic (Non-Exact) • Multilevel Synthesis Logic Expressions Ù Circuits f stv stwx styz uv uwx uyz =+ + + + + ( )( ) f st u wx yz v = ++ +
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2 UM EECS 270 Fall 2009 2-Level Circuits Assumptions: – Inputs are available in both true and complemented forms (reasonable assumption: FF outputs are available in both phases) – Gates have no fan-in or fan-out restrictions (unreasonable assumption: typically FI < 4, FO < 6) Correspond to SOP or POS forms of a switching function: –SO P Ù AND/OR (NAND/NAND) –PO S Ù OR/AND (NOR/NOR) # of 1st level AND (OR) gates = # of nontrivial product (sum) terms Fan-in of 2nd level OR (AND) gate = total # of product (sum) terms Usually implemented using regular structures: – Read-Only Memories (ROMs) – Programmable Logic Arrays (PLAs) AND/OR Ù NAND/NAND
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3 UM EECS 270 Fall 2009 Terminology Review Literal : A variable or its complement –E x : Product Term : A single literal or a product of two or more literals x : Sum of Products : A sum of product terms Minterm : A product term where every variable of the function appears once as a literal (i.e., in complemented or uncomplemented form) Canonical Sum : A sum of minterms. Every function has a unique canonical sum B Y X , , Z Y X W C B A XY , , Canonical Sum Representations Canonical sum uniquely defines a function, but can be long. A minterm list is a list of the row numbers of minterms included in the canonical sum. – Also known as the on-set Three canonical ways of representing functions – truth table – canonical sum – minterm list BC F 00 01 10 11 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 A = C B A F , , ) 7 , 6 , 2 (
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4 UM EECS 270 Fall 2009 Canonical Product Representation Sum Term : A single literal or a sum of two or more literals Product of Sums : A product of sum terms Maxterm : A sum term where every variable in the function appears once as a literal Canonical Product : A product of maxterms Maxterm List : A list of the truth table row numbers of the maxterms of a function – Also known as the off-set BC F 00 01 10 11 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 A 0 1 2 3 4 5 6 7 Row # ) )( )( ( C
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This note was uploaded on 04/18/2011 for the course EECS 270 taught by Professor David during the Spring '11 term at Michigan State University.

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270L19-Two+Level+Logic+Minimization - Logic Synthesis: From...

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