Number of representable values with 8-bit binary coding In an 8-bit digital representation of voltage levels, how many distinct codes (and thus distinct values) are available?

Introduction / Context:Bit depth determines the number of unique digital codes available to represent an analog quantity after quantization. More bits mean more discrete levels and generally finer resolution for a given full-scale range.

Given Data / Assumptions:

• Binary coding with 8 bits (N = 8).
• Unsigned representation (typical for raw ADC output codes).
• Ideal mapping between codes and levels (no missing codes).

Concept / Approach:

The number of distinct codes for N bits is 2^N. Each additional bit doubles the available codes. For 8 bits, this is 2^8 = 256 discrete codes, often corresponding to analog levels from code 0 to code 255 inclusive.

Step-by-Step Solution:

Verification / Alternative check:

Check consistency: 7 bits → 128 levels; 9 bits → 512 levels. The pattern confirms the exponentiation rule.

Why Other Options Are Wrong:

16, 64, 128 correspond to 4-, 6-, and 7-bit systems, respectively—not 8-bit.

Common Pitfalls:

Confusing number of codes with dynamic range or SNR; while more bits usually improve resolution, system noise and nonlinearity also matter.

Final Answer:

256