Resolution percent and bit count from DAC specs A DAC has a step size of 0.25 V and a full-scale output of 7.75 V. What are the percent resolution and the number of input bits?

Introduction / Context:
Given a DAC step size and full-scale (FS) output, we can deduce both the percentage resolution and the number of bits implemented by the converter.

Given Data / Assumptions:

• Step size = 0.25 V.
• Full-scale output FS = 7.75 V.

Concept / Approach:
Percent resolution = (step / FS) * 100%. The number of intervals across FS is FS / step. Number of codes (levels) equals intervals + 1, so bits n satisfy 2^n = levels.

Step-by-Step Solution:
Compute intervals: 7.75 / 0.25 = 31 intervals.Compute levels: 31 + 1 = 32 levels.Find bits: 2^n = 32 → n = 5 bits.Percent resolution: (0.25 / 7.75) * 100% ≈ 3.2258% ≈ 3.23%.

Verification / Alternative check:
LSB fraction of FS is 1 / (2^n − 1) = 1 / 31 ≈ 3.23%, consistent with the above computation.

Why Other Options Are Wrong:
31% corresponds to 1/3.23, not applicable here.Any 4-bit option is impossible because 4 bits provide only 16 levels.Other pairings mix the correct percent with the wrong bit count.

Common Pitfalls:
Forgetting to add one when converting intervals to levels; confusing resolution percent with accuracy.

Final Answer:
3.23%, 5 bits