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Equation 7 · How Edge AI Electronics and Sensor Systems Actually Work

What does this equation mean?

Pavg=d⋅Pactive+(1−d)⋅PsleepP_{\text{avg}} = d \cdot P_{\text{active}} + (1-d) \cdot P_{\text{sleep}}

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsd × P_active + (1-d) × P_sleep
Result or conditionP_avg
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

PavgP_{\text{avg}}

Symbol P_avg

PaP_avg is part of the quantity the equation computes from the expression on the right.

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dd

Symbol d

d is one of the signed contributions combined to compute the quantity on the left.

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PactiveP_{\text{active}}

Symbol P_active

PaP_active is one of the signed contributions combined to compute the quantity on the left.

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PsleepP_{\text{sleep}}

Symbol P_sleep

PsP_sleep is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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multiplication

multiplication

Multiply the quantities on either side.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

and the sustainable average power of an always-on system operating at duty cycle d (the fraction of time spent active rather than in a low-power sleep state) is Pavg=d⋅Pactive+(1−d)⋅PsleepP_{\text{avg}} = d \cdot P_{\text{active}} + (1-d) \cdot P_{\text{sleep}}. This identity is trivial algebraically, but it is exactly the trade a systems designer is making when choosing between “a bigger, slower model that runs less often” and “a smaller, faster model that still meets the same detection latency.” Neither PactiveP_{\text{active}} nor tactivet_{\text{active}} is fixed by the model architecture alone; both depend on the accelerator the model runs on.

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Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

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