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 ?

Vin = 1.992 V, 

n = 8

Vfs = 5 V

We know, from graph

Step size = $\frac{V_{fs}}{2^n-1}$

Step size = $\frac{5}{2^8-1}=\frac{5}{255}$

Analog input = Step size × (decimal equivalent of binary code)

$1.992=\frac{5}{255}\times D$

$D=\frac{1.992\times 255}{5}=(101.592{)}_{10}$

For decimal equivalent of 101, 

Analog input = $\frac{5}{255}\times 101=1.980$

Here 1.98 is less than 1.992 so, we have to take decimal equivalent as 102

For (102)₁₀ Analog input = $\frac{5}{255}\times 102=2$

2 is near about 1.992 so, decimal equivalent will 102 in hexadecimal, (102)₁₀ = 66 H