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Resolution of a 12-Bit ADC

A 12-bit analogue-to-digital converter has a full-scale reference of $V_{ref} = 5.0\ \text{V}$ .

Find the resolution — the voltage represented by one least significant bit.

Given

n	12 -	Resolution in bits
Vref	5 V	Full-scale reference

Hint 1

How many distinct output codes does an n-bit converter have?

Hint 2

2¹² = 4096 steps across the full-scale range.

Hint 3

LSB = V_ref/2ⁿ.

Worked solution — try the problem first

An $n$ -bit converter divides the full-scale range into $2^n$ steps:

$\text{LSB} = \frac{V_{ref}}{2^n} = \frac{5.0}{2^{12}} = \frac{5.0}{4096} = 1.221\times10^{-3}\ \text{V}$

$\boxed{\text{Resolution} = 1.221\ \text{mV}}$

Why $2^n$ and not $2^n - 1$ . A 12-bit converter has 4096 distinct output codes, spanning 4095 intervals. Dividing by 4096 gives the nominal step size and is the usual convention; dividing by 4095 gives 1.2210 mV — a 0.02% difference, negligible in practice but worth knowing when a datasheet specifies one or the other.

Each extra bit halves the step. A 16-bit converter on the same reference would resolve 76.3 μV.

Concepts:ADC resolutionQuantisationDigital systems

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