Bit depth vs. accuracy: If we increase bit width from 4 bits to 8 bits, does the conversion accuracy merely double?

Introduction / Context:Bit depth strongly affects resolution and potential accuracy in digital-to-analog conversion. This item tests intuition: moving from 4 to 8 bits increases code levels from 16 to 256, which is far more than a mere doubling of precision.

Given Data / Assumptions:

• Resolution (normalized) ≈ 1 / 2^n.
• 4-bit → 1/16; 8-bit → 1/256.
• “Relative accuracy” here refers to ideal quantization resolution absent nonidealities.

Concept / Approach:Doubling the number of bits increases resolution exponentially: each added bit halves the LSB size. Going from 4 to 8 bits adds 4 bits, yielding a 2^4 = 16× improvement, not 2×. Therefore, the statement that accuracy “doubles” is incorrect by an order of magnitude for ideal quantization limits.

Step-by-Step Solution:

Verification / Alternative check:Quantization noise power scales with LSB^2; adding 4 bits reduces quantization noise by 24 dB (approximately 6.02 dB/bit), far more than a 6 dB “doubling.”

Why Other Options Are Wrong:

Common Pitfalls:Confusing absolute accuracy (affected by INL/DNL, reference tolerance) with bit-limited resolution; assuming linear rather than exponential scaling with additional bits.

Final Answer:Incorrect