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Timing Analysis Predicated on a topological ordering. l 1 = 1 level: l 2 = 1 x y x y z z c s g1g1 g4g4 g3g3 g2g2 g5g5 l 3 = 2 l 5 = 2 l 4 = 3

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z 1010 1010 1010 1010 1010 1212 0202 1212 Timing Analysis Predicated on a topological ordering. 1 0101 x y x y z c s arrival times 1010 (assume a delay bound of 1 time unit for each gate) l 1 = 1 l 2 = 1 g4g4 g3g3 g2g2 g5g5 l 3 = 2 l 5 = 2 l 4 = 3 g1g1 level:

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Circuit Model Perform static analysis in the “floating-mode”. At the outset: all wires are assumed to have unknown/undefined values ( ). the primary inputs assume definite values in {0, 1}. a “controlling” input full set of “non-controlling” inputs unknown/undefined output

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Circuit Model During the analysis, only signals driven (directly or indirectly) by the primary inputs are assigned definite values. 1 ORAND Perform static analysis in the “floating-mode”. At the outset: all wires are assumed to have unknown/undefined values ( ). the primary inputs assume definite values in {0, 1}.

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Circuit Model AND Up-bounded inertial delay model. each gate has delay in [ 0, t d ] Ensures monotone speed-up property.

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Circuit Model The arrival time at a gate output is determined: either by the earliest controlling input. AND 1313 0202 0606 0303 (assuming a delay bound of 1)

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Circuit Model The arrival time at a gate output is determined: either by the earliest controlling input; AND 1313 1212 1616 or by the latest non-controlling input. 1717 (assuming a delay bound of 1)

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Analysis Functional Analysis: determine what is computed. Timing Analysis: determine how long it takes to compute it. level: l 1 = 1 l 2 = 1 l 3 = 2 l 5 = 2 l 4 = 3 a b a b g1g1 g2g2 g3g3 g4g4 g5g5 c c 1010 1010 1010 1010 1010 1212 0202 1212 1 0101 1010

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Analysis Explicit analysis: ORAND Functional Analysis: determine what is computed. Timing Analysis: determine how long it takes to compute it.

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ORAND 000 0101 0202 0101 Analysis000 0101 0202 0101 Explicit analysis: Functional Analysis: determine what is computed. Timing Analysis: determine how long it takes to compute it.

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0202 000 0101 0202 0101 ORAND 0 10100 0101 0303 m inputs explict evaluation intractable combinations; Analysis000 0101 0202 0101 00 1010 0101 0202 0303 Explicit analysis: Functional Analysis: determine what is computed. Timing Analysis: determine how long it takes to compute it.

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ORAND Analysis 0 0202 10100 0101 0303 Symbolic analysis: binary, multi-terminal decision diagrams. 0 1 0101 0202 ? 1313 Functional Analysis: determine what is computed. Timing Analysis: determine how long it takes to compute it.

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Lecture 11 Timing diagrams Hazards.

Lecture 11 Timing diagrams Hazards.

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