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Equation 3 · How Edge AI Electronics and Sensor Systems Actually Work

What does this equation mean?

q=Vref2Nq = \frac{V_{ref}}{2^{N}}

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Start withV_ref
Divide by2^N
This relates toq
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.

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qq

Symbol q

the size of one quantization step.

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VrefV_{ref}

Symbol V_ref

VrV_ref occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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NN

Symbol N

N occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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=

=

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

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fraction

fraction

Divide the expression above the line by the one below 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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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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2N2^{N}

Denominator: 2^N

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

The quantization step itself has a clean expression once gain and reference voltage are fixed. For an ADC with N effective bits resolving a full-scale reference voltage VrefV_{ref} , the size of one quantization step is q=Vref2Nq = \frac{V_{ref}}{2^{N}}. and, treating quantization error as uniformly distributed over one step, the resulting quantization noise power has a root-mean-square value of q / 12\sqrt{12} . This is the textbook derivation behind every “effective number of bits” figure a converter data sheet reports, and it is the reason oversampling helps: spreading the same quantization noise power across a wider sampled bandwidth before filtering it back down effectively lowers the in-band noise floor…
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The quantization step itself has a clean expression once gain and reference voltage are fixed. For an ADC with N effective bits resolving a full-scale reference voltage VrefV_{ref} , the size of one quantization step is q=Vref2Nq = \frac{V_{ref}}{2^{N}}. and, treating quantization error as uniformly distributed over one step, the resulting quantization noise power has a root-mean-square value of q / 12\sqrt{12} . This is the textbook derivation behind every “effective number of bits” figure a converter data sheet reports, and it is the reason oversampling helps: spreading the same quantization noise power across a wider sampled bandwidth before filtering it back down effectively lowers the in-band noise floor without changing the converter’s physical resolution. This is analysis grounded in a standard result, not a claim from either vendor’s marketing copy — both data sheets report measured effective noise in microvolts or nanovolts RMS directly, and those measured numbers are what a systems designer should budget against, not the nominal bit count printed on the package.

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