Resolution of a 4-bit DAC — value of the least significant bit (LSB) For a 4-bit digital-to-analog converter, the LSB step size corresponds to what percentage of the full-scale range?

Introduction / Context:
The resolution of a DAC indicates the smallest analog change produced by a 1-bit change in the digital input. For an N-bit DAC, this smallest increment—one least significant bit (LSB)—is a fixed fraction of the full-scale output range.

Given Data / Assumptions:

• N = 4 bits.
• Full-scale (FS) is the maximum span of the DAC output.
• Ideal DAC behavior (no nonlinearity or offset errors).

Concept / Approach:

For an N-bit DAC, the LSB size in percent is 100% / 2^N. This comes from the fact that there are 2^N distinct codes, and adjacent codes differ by exactly one LSB step in an ideal DAC.

Step-by-Step Solution:

Verification / Alternative check:

Cross-check: a 3-bit DAC would have 1/8 = 12.5% per LSB; increasing bit count halves the LSB percentage per additional bit, consistent with 4-bit giving 6.25%.

Why Other Options Are Wrong:

0.625% corresponds roughly to 8-bit resolution (1/160 ≈ 0.625%), not 4-bit. 12% and 1.2% do not match any power-of-two fraction for 4 bits.

Common Pitfalls:

Confusing LSB size with full-scale range; forgetting that resolution improves exponentially with each added bit.

Final Answer:

6.25% of full scale