Analog signals — counting possibilities over a continuous range. If an analog signal can vary anywhere between 0 V and 5 V, how many distinct analog values are possible in theory?

Introduction / Context:
Analog signals, in theory, can assume any real-valued amplitude within a specified range. Unlike digital signals that restrict values to a finite set of levels, analog amplitudes are continuous, leading to an uncountably infinite set of possibilities in mathematics (within noise and bandwidth limits in practice).

Given Data / Assumptions:

• Amplitude limits: 0 V to 5 V inclusive.
• Idealized measurement (no quantization, infinite resolution).
• No discretization via ADC is applied.

Concept / Approach:
A continuous interval on the real number line contains infinitely many values. Any subinterval, no matter how small, can be subdivided indefinitely. Therefore, the theoretical count of distinct analog levels is infinite. Finite counts only appear after quantization (e.g., an N-bit ADC yields 2^N discrete codes).

Step-by-Step Reasoning:

Verification / Alternative check:
Compare with a 10-bit ADC: 2^10 = 1024 discrete codes approximate 0–5 V but do not make it truly continuous. Removing quantization restores the infinite set. Laboratory instruments with higher resolution approach but never reach perfect continuity; the theoretical model remains infinite.

Why Other Options Are Wrong:

• 5, 50, 250, 1024: each presumes discretization (step counts). These apply only when a quantizer (ADC, DAC step size) is specified.

Common Pitfalls:

• Confusing device resolution (finite) with the mathematical nature of analog signals (continuous).

Final Answer:
infinite