Digital-to-Analog Converter (DAC) fundamentals For a DAC with 6-bit resolution, how many distinct output voltage levels (quantization steps) are possible across its full-scale range?

Introduction / Context:
A Digital-to-Analog Converter (DAC) translates a digital code into an analog voltage or current. The resolution, expressed in bits, determines how finely the full-scale analog range is divided into discrete steps. Knowing how to compute the number of output levels from the bit resolution is essential in instrumentation, audio, and control systems.

Given Data / Assumptions:

• Resolution = 6 bits.
• Each additional bit doubles the number of representable codes.
• All codes from 0 to full-scale are assumed to be valid and monotonic.

Concept / Approach:

The number of unique output levels a DAC can produce equals the number of unique input codes. For an n-bit binary code, there are 2^n distinct codes. These codes map to equally spaced analog levels (ignoring nonidealities such as offset, gain error, and DNL/INL).

Step-by-Step Solution:

Verification / Alternative check:

Sanity check by halving and doubling: 4 bits → 16 levels; 8 bits → 256 levels. Six bits lies between these (16 and 256), specifically at 64, which is consistent.

Why Other Options Are Wrong:

• 6: Confuses bit count with level count.
• 16: Corresponds to 4 bits, not 6.
• 32: Corresponds to 5 bits, not 6.

Common Pitfalls:

• Mixing up levels and steps size. The number of levels is 2^n, while the step size depends on full-scale range / (2^n − 1).
• Assuming non-binary coding. Standard binary-weighted DACs still yield 2^n levels regardless of coding scheme used upstream.

Final Answer:

64