An analog voltage is in the range of 0 to 8 V is divided in eight equal intervals for conversion to 3-bit digital output. The maximum quantization error is

Concept:

The concept of converting an analog signal to its digital counterpart is explained with the help of the following diagram:

∴ The maximum quantization is given as:

\({Q_{e\left( {max} \right)}} = \frac{{\rm{\Delta }}}{2}\)

Δ = step size given by:

\({\rm{\Delta }} = \frac{{{V_{max}} - {V_{min}}}}{L}\)

L = Number of levels

Calculation:

With n = 3, the number of levels will be:

L = 2³ = 8

With analog input in the range 0 to 8 V and L = 8, the step size will be:

\({\rm{\Delta }} = \frac{{8 - 0}}{{8}} = 1\)

Now, the maximum quantization error will be:

\({Q_{e\left( {max} \right)}} = \frac{{1}}{2} = 0.5\)