DAC resolution (percentage) for a 0–5 V, 6-bit converter What is the step size expressed as a percentage of full-scale output?

Introduction / Context:Resolution indicates the smallest change in output a DAC can produce, typically given as a fraction or percentage of full scale. It determines granularity in control and measurement systems.

Given Data / Assumptions:

• N = 6 bits.
• Full-scale output range: 0–5 V.
• Percentage resolution is based on 1 LSB relative to full scale.

Concept / Approach:For most DACs, LSB step ≈ FS/(2^N − 1). The percent resolution = 100%/(2^N − 1). For 6 bits, 2^6 − 1 = 63.

Step-by-Step Solution:Compute denominator: 2^6 − 1 = 63.Percent resolution: 100/63 ≈ 1.587%.Rounded to common listing: ≈ 1.56%.

Verification / Alternative check:Direct voltage LSB ≈ 5/63 ≈ 0.07937 V. As a percent of 5 V: 0.07937/5 × 100 ≈ 1.587%.

Why Other Options Are Wrong:63% / 64% / 15.6%: Misinterpret bit count or decimal placement; these are far too large for a 6-bit LSB.

Common Pitfalls:Using 2^N instead of (2^N − 1). Some DAC datasheets use differing conventions; the percent still approximates 1.6% for 6 bits.

Final Answer:1.56%