Output level count of a basic 4-bit DAC A basic 4-bit digital-to-analog converter can produce how many distinct output values, and are those values proportional to the binary input?
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A16 different values of voltage or current that are not proportional to the input binary number
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B16 different values of voltage or current that are proportional to the input binary number
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C32 different values of voltage or current that are not proportional to the input binary number
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D32 different values of voltage or current that are proportional to the input binary number
Answer
Correct Answer: 16 different values of voltage or current that are proportional to the input binary number
Explanation
Introduction / Context:Resolution and proportionality are fundamental DAC characteristics. A 4-bit converter’s output range is quantized into a finite number of equally spaced steps proportional to the digital code.
Given Data / Assumptions:
- Resolution N = 4 bits.
- Unipolar ideal DAC behavior assumed.
Concept / Approach:An ideal N-bit DAC produces 2^N discrete output levels. For N = 4, there are 16 distinct values. These values are proportional to the input code, spaced by one LSB (Vref / 2^N for voltage-mode).
Step-by-Step Solution:
Compute levels: 2^4 = 16.Note proportionality: Vout = (Code / 2^N) * Vref (or scaled current mode).Conclude 16 proportional output levels.Verification / Alternative check:Enumerate codes 0000 through 1111 → 16 unique outputs from zero to near full-scale.
Why Other Options Are Wrong:
- 32 values: Would require 5 bits.
- Not proportional: Ideal DAC outputs are proportional to the input code.
Common Pitfalls:
- Confusing number of codes (2^N) with number of steps between codes (2^N − 1 intervals).
Final Answer:16 different values of voltage or current that are proportional to the input binary number