Question E8A09:
How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?  

Choices:  
A: 8  
B: 8 multiplied by the gain of the input amplifier  
C: 256 divided by the gain of the input amplifier  
D: 256    

Correct Answer is  D: 256  

Correct answer: D — 256

Why D is correct:
- An N-bit ADC can represent $2^N$ distinct codes (levels).
- For 8 bits:  
  $$\text{Levels} = 2^N = 2^8 = 256$$

Why the other choices are incorrect:
- A: 8 — Confuses number of bits with number of levels. 8 bits means 8 binary digits, not 8 levels.
- B: 8 multiplied by the gain of the input amplifier — The amplifier gain changes the input voltage range seen by the ADC but does not change the number of digital codes. The code count is fixed by the number of bits.
- C: 256 divided by the gain of the input amplifier — Same issue: gain affects scaling, not the number of possible codes.

Useful formulas and rules of thumb:
- Number of levels: $$\text{Levels} = 2^N$$
- LSB size (quantization step) for full-scale range $V_{\text{FS}}$: $$\Delta V_{\text{LSB}} = \frac{V_{\text{FS}}}{2^N}$$
- Each additional bit doubles the number of levels and improves ideal quantization SNR by about $6.02$ dB:  
  $$\text{SNR}_{\text{quant}} \approx 6.02N + 1.76\ \text{dB}$$