Consider the following statements regarding ADC characteristics:1.Resolution of an ADC is defined as the smallest change in analog input that can be detected and is inversely proportional to number of bits.2.Quantization error is inherent in ADC and cannot be completely eliminated but can be minimized by increasing resolution.3.Sampling rate has no effect on signal reconstruction quality in digital systems.Which of the above statements is/are correct?

Correct Answer: B - 2 only

Quick Concept Explanation

An ADC discretizes both amplitude and time. Bit depth controls amplitude resolution; sampling frequency controls temporal/spectral resolution and aliasing. Key relation: LSB ≈ VFS/2^n (or VFS/(2^n−1), depending convention); ideal quantization error ≈ ±0.5 LSB; sampling theorem requires fs > 2fmax for ideal band-limited reconstruction.

Exam focus: Bits → amplitude resolution. Sampling rate → aliasing/reconstruction. Common trap: Saying “more bits means resolution is 1/n”; it is approximately one part in 2^n.

Statement-wise Verification

• Statement 1 - Incorrect.
  Resolution of an ADC is defined as the smallest change in analog input that can be detected and is inversely proportional to number of bits.
  As worded: the smallest quantization step decreases exponentially with bit count, approximately as 1/2^n, not as 1/n. The definition part is reasonable, but the stated proportionality makes the full statement false.
• Statement 2 - Correct.
  Quantization error is inherent in ADC and cannot be completely eliminated but can be minimized by increasing resolution.
  Finite quantization creates unavoidable quantization error; more bits reduce LSB size and therefore reduce ideal quantization uncertainty.
• Statement 3 - Incorrect.
  Sampling rate has no effect on signal reconstruction quality in digital systems.
  Sampling rate determines whether spectral replicas overlap (aliasing) and therefore directly affects reconstructability.

Core Concept

An ADC discretizes both amplitude and time. Bit depth controls amplitude resolution; sampling frequency controls temporal/spectral resolution and aliasing. These are separate limitations and should never be mixed.

Formula / Key Relationship

LSB ≈ VFS/2^n (or VFS/(2^n−1), depending convention); ideal quantization error ≈ ±0.5 LSB; sampling theorem requires fs > 2fmax for ideal band-limited reconstruction.

Step-by-Step Check

Mathematical dependence 2^n disproves the “inverse to number of bits” wording. Nyquist reasoning disproves statement 3. Only statement 2 survives, so B.

Why the Other Options Are Wrong

Option A is incorrect because it includes incorrect statement(s) 1. Option C is incorrect because it includes incorrect statement(s) 1, 3 and omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 1, 3.

Answer-Key Verification Note

The uploaded provisional key marks D . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.

Common Mistake

Saying “more bits means resolution is 1/n”; it is approximately one part in 2^n.

Quick Revision

ADC Resolution Quantization and Samplingis linked with Analog-to-Digital Conversion, Data Converters and Digital Electronics. Bits → amplitude resolution. Sampling rate → aliasing/reconstruction.