Flash Analog-to-Digital Converter (ADC): Determine the resolution (LSB size) when 15 comparators are used with a 10 V reference.

Introduction / Context:
Flash ADCs use many comparators in parallel to achieve very high conversion speeds. The number of comparators determines the resolution (number of bits) and the least significant bit (LSB) size for a given reference range. This problem explores that relationship.

Given Data / Assumptions:

• Number of comparators: 15.
• Reference range (full-scale): 0 to 10 V.
• Ideal, uniform quantization; thermometer-to-binary encoding.

Concept / Approach:

In a flash ADC, the number of comparators N_c relates to the number of bits n by N_c = 2^n − 1. Once n is found, the LSB size (resolution) is V_ref / 2^n for an n-bit converter.

Step-by-Step Solution:

Verification / Alternative check:

Check with code count: There are 16 quantization levels (0000 to 1111). Each step is 10 V / 16 = 0.625 V, consistent with the calculation.

Why Other Options Are Wrong:

• 0.656 V and 0.525 V: Numerical distractors; do not match 10/16.
• Insufficient data: Not true; comparators fully determine n.
• 1.000 V: Would correspond to a 10-level (non-binary) or 10-bit-per-volt interpretation; not applicable.

Common Pitfalls:

• Confusing the number of comparators with the number of levels (remember the −1).
• Using 2^(n−1) instead of 2^n in the denominator when computing LSB.

Final Answer:

0.625 V