Converter usefulness criterion: “For A/D and D/A converters to be useful, there must be a meaningful mapping between the analog quantity and its digital representation, and vice versa.” Determine whether this statement is valid.

Introduction / Context:
Converters bridge the analog and digital realms. Their utility rests on a predictable, calibrated relationship between physical quantities (voltage, current, temperature via sensors) and digital codes (binary words). Without a defined mapping, measurements and actuations would be uninterpretable.

Given Data / Assumptions:

• ADC: maps analog input to digital code using a transfer function.
• DAC: maps digital code to analog output using a reconstruction function.
• “Meaningful” implies monotonicity, documented scaling, and tolerances.

Concept / Approach:
A converter’s transfer function defines the code-to-quantity relationship. Linearity (or a known nonlinearity), gain/offset, monotonicity, resolution, and noise determine how well codes represent real-world values. Calibration or specifications ensure that a given code corresponds to a predictable analog value within error bounds. The reverse mapping must be equally defined so a desired analog level can be commanded digitally. Therefore, the statement captures the essence of converter utility.

Step-by-Step Solution:

Verification / Alternative check:
Calibration procedures and datasheet specs (gain, offset, INL/DNL, noise) provide the mapping accuracy that systems rely on for sensing and control.

Why Other Options Are Wrong:

• Incorrect: Would deny the fundamental purpose of converters.
• Only true for linear converters: Nonlinear mappings are also “meaningful” if defined.
• Ambiguous: Coding (offset binary, two’s complement) still yields a documented mapping.

Common Pitfalls:
Confusing resolution with accuracy; ignoring reference stability and calibration in defining the mapping.

Final Answer:
Correct