Question

An 8-bit ADC converts analog voltage in the range of 0 to +5 V to the corresponding digital code as per the conversion characteristics shown in figure. For \(V_{in} = 1.9922 \, V\), which of the following digital output, given in hex, is true? \begin{center} \includegraphics[width=0.55\textwidth]{18.jpeg} \end{center}

• A. 64H
• B. 65H
• C. 66H
• D. 67H

Hint:

For ADC problems: First find step size \(\Delta = \frac{V_{ref}}{2^n}\), then compute the digital equivalent by dividing input by step size, and finally convert to hex.

Answer 1

The Correct Option is C

Step 1: Resolution of 8-bit ADC.
For 8-bit: \[ 2^8 = 256 \, \text{levels} \] Input range: \(0 \to 5 \, V\). Thus, step size: \[ \Delta = \frac{5}{256} = 0.01953 \, V = 19.53 \, mV \]

Step 2: Equivalent digital count.
For \(V_{in} = 1.9922 \, V\): \[ N = \frac{V_{in}}{\Delta} = \frac{1.9922}{0.01953} \approx 102 \]

Step 3: Convert to hex.
Decimal 102 = Hex \(66\).

Step 4: Final result.
Thus, the ADC output is: \[ \boxed{66H} \]