Flash (parallel-encoded) ADC sizing For converting an analog signal to 8-bit resolution using a flash (parallel-encoded) ADC, how many comparators are required?

Introduction / Context:
Flash ADCs achieve extremely fast conversion by comparing the input simultaneously against many reference levels. The hardware cost scales exponentially with resolution, so computing the number of comparators is key to feasibility assessments.

Given Data / Assumptions:

• Resolution N = 8 bits.
• Ideal flash topology (thermometer code) using a resistor ladder and comparators.

Concept / Approach:
A flash ADC requires 2^N − 1 comparators to create 2^N distinct quantization levels. Each comparator checks if Vin exceeds a specific threshold; their outputs form a thermometer code then encoded to binary.

Step-by-Step Solution:
Compute 2^N: 2^8 = 256 levels.Number of comparators = 2^N − 1 = 256 − 1.So, comparators required = 255.

Verification / Alternative check:
Check small N: for N=3, levels=8, comparators=7. Pattern holds, confirming the formula for N=8.

Why Other Options Are Wrong:

• 127 or 128 or 256: Do not match 2^8 − 1.

Common Pitfalls:

• Forgetting to subtract 1 from 2^N.
• Confusing number of levels with number of comparators.

Final Answer:
255