Finer Steps Reduce the Reconstruction Error - Electronic Circuits X: Sampling, Quantization, and Finite Conversion Step by Step

A smaller LSB can reduce the exact reconstruction error. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A one-volt LSB leaves half a volt of error

Input 11/2 volts reconstructs to 5 volts on the coarse ladder.

{11\over 2}\ \text{V}\ -\ 5\ \text{V}={1\over 2}\ \text{V}

A half-volt LSB can hit the same input exactly

With LSB 1/2 volt, code 11 reconstructs exactly 11/2 volts.

11\cdot {1\over 2}\ \text{V}={11\over 2}\ \text{V}