An n-bit DAC has a full-scale (reference) of 5 V and a resolution (LSB size) of 5 mV. What is the value of n?

Introduction / Context:
DAC resolution links the number of bits to the smallest analog step size. Correctly relating LSB size to full-scale range is fundamental in data conversion design.

Given Data / Assumptions:

• Vref (full-scale) = 5 V.
• Resolution (LSB) = 5 mV = 0.005 V.
• Assume ideal straight-binary coding.

Concept / Approach:

Two common definitions exist: LSB = Vref / (2^n) or LSB = Vref / (2^n - 1). For ideal sizing and most quick estimates, LSB ≈ Vref / 2^n suffices. Using this yields a clean integer n.

Step-by-Step Solution:

Verification / Alternative check:

A 10-bit DAC has 1024 steps; LSB ≈ 5 / 1024 ≈ 4.88 mV, very close to 5 mV; the stated resolution is consistent with 10 bits.

Why Other Options Are Wrong:

• 8, 9 bits: yield LSBs significantly larger than 5 mV.
• 11 bits: LSB would be roughly 2.44 mV, smaller than specified.

Common Pitfalls:

Confusing Vref/(2^n) and Vref/(2^n - 1); both give n ≈ 10 here, but always check the convention used in the specific DAC's datasheet.

Final Answer:

10