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?

Difficulty: Easy

Correct Answer: 256

Explanation:


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:

Identify bit width N = 8.Compute 2^N = 2^8 = 256.Interpretation: 256 unique digital values (codes 0–255).


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

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