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218L8S09

# 218L8S09 - ESE218 Lecture 8 Gate-level minimization...

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2/19/09 ESE218 Spring 2009 Lecture 8 1 ESE218 Lecture 8. Gate-level minimization. Glitch-free design. Incompletely specified functions. Outline ± Primary implicants and function covers ± Consensus property ± Race conditions and hazards ² static-0 and static-1 glitches ² glitch-free design ± Iterated consensus ± Functions with don’t cares ± Summary

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2/19/09 ESE218 Spring 2009 Lecture 8 2 Canonical standard forms 7 6 5 4 3 2 1 0 # 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 G(X,Y,Z) Z Y X Sum-of-minterms Product-of-maxterms G = XY’ + Z = = + + + + = ) 7 , 5 , 4 , 3 , 1 ( ) , , ( 7 5 4 3 1 m m m m m Z Y X G ) 6 , 2 , 0 ( ) , , ( 6 2 0 = = M M M Z Y X G = = ) 7 , 5 , 4 , 3 , 1 ( ) 6 , 2 , 0 ( ) , , ( Z Y X G Complement to the function:
2/19/09 ESE218 Spring 2009 Lecture 8 3 Primary implicants and function covers F = A C + B C’ + AB = A C + B C’ m 7 m 3 m 5 m 1 m 6 m 4 m 2 m 0 BC A 0 1 01 00 11 10 1 1 1 1 BC A 0 1 01 00 11 10 Implicants: m 2 , m 5 m 6 , m 7, AC, BC’, AB Primary implicants: AC, BC’, AB Essential primary implicants: AC, BC’ AC BC’ AB

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2/19/09 ESE218 Spring 2009 Lecture 8 4 Consensus property A C + B C’ + AB = A C + B C’ m 7 m 3 m 5 m 1 m 6 m 4 m 2 m 0 BC A 0 1 01 00 11 10 1 1 1 1 BC A 0 1 01 00 11 10 F(A,B,C) = Σ (2,5,6,7) AC BC’ AB A and B can be algebraic expressions
2/19/09 ESE218 Spring 2009 Lecture 8 5 Should one keep or remove the consensus term? 2-to1 MUX: F=A if C =1 or F=B if C=0 1 1 1 1 BC A 0 1 01 00 11 10 AC BC’ Racing conditions can lead to glitches 4 5 6 7408 1 2 3 7408 1 2 3 7432 1 2 7404 C A = 1, B = 1 F C B A AC BC’ F BC’ AC A momentary 0 output may occur during transition of one of the input variables

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2/19/09 ESE218 Spring 2009 Lecture 8 6 Elimination of static-1 hazards 4 5 6 7408 9 10 8 7408 1 2 3 7408 1 2 3 1 2 7404 A C + B C’ = A C + B C’ + AB 1 1 1 1 BC A 0 1 01 00 11 10 AC BC’ AB SOP implementations can lead to static-1 hazards Additional term AB eliminates the static-1 hazard in SOP implementations
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218L8S09 - ESE218 Lecture 8 Gate-level minimization...

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