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# 电子工程代写|数字系统设计代写Digital System Design代考|EE108 Time Behavior of Combinational Networks

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## 电子工程代写|数字系统设计代写Digital System Design代考|Deﬁﬁnitions and Timing Models

A logical gate introduces a delay between the change in value of the input and that of the output. In the figure below, the input and output signals of a NOT are represented in idealized form, since the transitions between logical values are instantaneous.

The delays in this form are called transport delays. This idealized model makes them quick and easy to read.
For simplicity’s sake, we could denote propagation times generically as:
$$t_p=\max \left(t_{P L H}, t_{P L H}\right)$$
When necessary, it is useful to adopt a more realistic signal model where level transitions (edges) do not occur instantly (in 0 time) but in finite times with linear progression. We use this model to describe inertial delays:

With this model, we assume that the logical level transitions occur when the signal reaches (rises to or lowers to) $50 \%$ of its excursion.

Propagation times $t_{P H L}$ and $t_{P L H}$ are the times between the signal-level transition at input and that at output.

## 电子工程代写|数字系统设计代写Digital System Design代考|Hazards

As we have seen, combinational networks can give rise to impulsive behavior due to differences in delays. These behaviors are called hazards. Depending on the physical component’s technology, these behaviors might be mitigated or removed by the inertial behavior of the circuits. In any case, these phenomena are potentially damaging due to their effect on the circuits that receive them and they should be avoided when they can cause errors.

The hazards that arise due to asymmetrical delay paths, due in turn to the presence of inverters or other gates, are called static hazards. They can generally be eliminated (or masked) through algebraic methods like the one explained later.

In the figure above, a simple network made up of an AND gate and a NOT gate allows us to observe the effect of different paths.

This network should generate a constant $(O U T=I N \cdot \overline{I N}=0)$. To perform a simplified time analysis, let us only consider transport delays so that the hazard will not be masked by the inertial delay.

## 电子工程代写|数字系统设计代写DIGITAL SYSTEM DESIGN代 考|DEFIFINITIONS AND TIMING MODELS

$$t_p=\max \left(t_{P L H}, t_{P L H}\right)$$

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