Eight-bit DAC resolution claim: “An 8-bit D/A converter has a resolution of 0.125.” Evaluate the accuracy; state the correct resolution as a fraction and percentage of full scale.

Introduction / Context:Resolution defines the smallest analog change a DAC can produce for a one-code increment, expressed as a fraction of full scale (FS) or as a percentage. Correctly calculating resolution is foundational in sizing converters for measurement and control applications.

Given Data / Assumptions:

• N = 8 bits.
• Ideal DAC with 2^N discrete levels.
• Resolution refers to 1 LSB relative to FS.

Concept / Approach:For an N-bit DAC, the number of codes is 2^N. The LSB size, as a fraction of full scale, is 1 / (2^N). Thus, for N = 8, resolution = 1 / 256 ≈ 0.00390625 FS, which equals 0.390625%. The claim “0.125” (unitless) does not match any standard expression for 8-bit resolution; 0.125 corresponds to 1/8 or 12.5%, which would be the resolution of a 3-bit DAC (1/2^3).

Step-by-Step Solution:

Verification / Alternative check:General formula holds for all N: Resolution% = 100 / (2^N). For N = 3, this gives 12.5% (0.125), confirming that 0.125 aligns with 3-bit, not 8-bit resolution.

Why Other Options Are Wrong:

• Correct: Would imply 8-bit steps of 12.5% FS—clearly incorrect.
• Only true for 3-bit DACs: This is a helpful comparison but the stem claims 8-bit.
• Ambiguous: Even without units, 0.125 as a fraction or decimal is not 1/256.

Common Pitfalls:Confusing number of levels (2^N) with number of steps (2^N − 1); forgetting to specify units (fraction vs percent) leading to misinterpretation.

Final Answer:Incorrect