6-bit DAC resolution as a percentage of full-scale For a 6-bit digital-to-analog converter, what is the nominal resolution expressed as a percentage of full-scale output?

Introduction / Context:Resolution describes the smallest output step a DAC can produce. For an N-bit DAC, the ideal LSB step equals full-scale divided by 2^N. Expressing this step as a percentage of full-scale is useful for quick error budgeting.

Given Data / Assumptions:

• N = 6 bits.
• Ideal behavior assumed (no nonlinearity, offset, or gain error).

Concept / Approach:Ideal resolution (LSB) fraction = 1 / 2^N. For N = 6, 1 / 64 = 0.015625 (unitless). Converting to percent gives 1.5625%. Rounding to the provided choices yields approximately 1.59%.

Step-by-Step Solution:Compute 2^6 = 64.Compute LSB fraction = 1 / 64 = 0.015625.Convert to percent → 0.015625 * 100% = 1.5625% ≈ 1.59%.

Verification / Alternative check:Some texts use 1 / (2^N − 1) for code steps across the full code range. For large N, the two are nearly identical. For N = 6, the difference is minor; 1 / 63 ≈ 1.587%.

Why Other Options Are Wrong:

• 63% or 64%: Those correspond to code counts, not resolution step size.
• 15.9%: Off by a factor of 10.

Common Pitfalls:Confusing resolution with accuracy or INL/DNL; resolution is about step size only.

Final Answer:1.59%