Digital vs. analog representations Which statement best describes digital representations of numerical quantities in instrumentation and computing systems?

Introduction / Context:
Digital systems encode information using discrete states (often 0 and 1) rather than continuously variable signals. Understanding the difference between discrete-step digital representations and continuous analog representations is foundational for studying data converters, logic design, and digital signal processing.

Given Data / Assumptions:

• The question contrasts how digital values behave compared to analog values.
• We assume ideal digital levels (noise margins, quantization) and typical binary encoding.

Concept / Approach:
Digital quantities change in discrete increments (quantization levels). The numeric value is represented by a finite set of code words (e.g., binary numbers). As the underlying physical quantity changes, the digital code updates stepwise, not continuously. This property enables robust storage, computation, and transmission with error detection/correction.

Step-by-Step Solution:

Verification / Alternative check:
A digital voltmeter with 12-bit ADC shows counts from 0 to 4095. As input increases, the display steps through integer codes; the change is not continuous but quantized, confirming the stepwise nature.

Why Other Options Are Wrong:

• Continuously changing / continuous range: describes analog, not digital.
• Constant and direct proportion without steps: ignores quantization; more analog-like.
• “Difficult to interpret” is subjective and not a defining property of digital data.

Common Pitfalls:
Confusing sampling (time discretization) with quantization (amplitude discretization). Digital systems may sample continuously changing analog signals but still represent them in discrete amplitude steps.

Final Answer:
that vary in discrete steps in proportion to the values they represent.