1.
Calculate the step size for an 8-bit ADC, given \(V_{ref} = 1.28~\textrm{V}\text{.}\)
Solution.
\begin{equation*}
\Delta V = \frac{V_{ref}}{2^n} = \frac{1.28~\textrm{V}}{2^{8}} = \frac{1.28~\textrm{V}}{256} = 5~\textrm{mV}
\end{equation*}
Exercises 6.6 Practice Problems
2.
Given the situation described in Exercise 6.6.1, calculate the output if the analog input is \(V_{in} = 0.7~\textrm{V}\text{.}\)
Solution.
\begin{equation*}
\textrm{value} = 2^n \left(\frac{V_{out}}{V_{ref}}\right) = 2^8 \left(\frac{0.7~\textrm{V}}{1.28~\textrm{V}}\right) = 140_{10} = 10001100_2
\end{equation*}
3.
Given the situation described in Exercise 6.6.1, calculate the output if the analog input is \(V_{in} = 1.0~\textrm{V}\text{.}\)
Solution.
\begin{equation*}
\textrm{value} = 2^n \left(\frac{V_{out}}{V_{ref}}\right) = 2^8 \left(\frac{1.0~\textrm{V}}{1.28~\textrm{V}}\right) = 200_{10} = 11001000_2
\end{equation*}
4.
How many bits of resolution does the ADC on the ATmega328P microcontroller have?
5.
True or false: The output of most sensors is analog.
Calculate the step size for the following ADCs, given \(V_{ref} = 5~\textrm{V}.\)
6.
8-bit ADC
Solution.
\begin{equation*}
\Delta V = \frac{V_{ref}}{2^n} = \frac{5~\textrm{V}}{2^{8}} = \frac{5~\textrm{V}}{256} = 19.5~\textrm{mV}
\end{equation*}
7.
10-bit ADC
Solution.
\begin{equation*}
\Delta V = \frac{V_{ref}}{2^n} = \frac{5~\textrm{V}}{2^{10}} = \frac{5~\textrm{V}}{1024} = 4.9~\textrm{mV}
\end{equation*}
8.
12-bit ADC
Solution.
\begin{equation*}
\Delta V = \frac{V_{ref}}{2^n} = \frac{5~\textrm{V}}{2^{12}} = \frac{5~\textrm{V}}{4096} = 1.2~\textrm{mV}
\end{equation*}
9.
16-bit ADC
Solution.
\begin{equation*}
\Delta V = \frac{V_{ref}}{2^n} = \frac{5~\textrm{V}}{2^{16}} = \frac{5~\textrm{V}}{65536} = 76.3~\mu\textrm{V}
\end{equation*}
Given \(V_{ref} = 2.56~\textrm{V}\text{,}\) calculate the corresponding analog voltage for each of the 8-bit ADC outputs.
10.
11111111
Solution.
\begin{equation*}
V_{out} = V_{ref} \left(\frac{\textrm{value}}{2^n}\right) = 2.56~\textrm{V} \left(\frac{255}{2^8}\right) = 2.55~\textrm{V}
\end{equation*}
11.
10011001
Solution.
\begin{equation*}
V_{out} = V_{ref} \left(\frac{\textrm{value}}{2^n}\right) = 2.56~\textrm{V} \left(\frac{153}{2^8}\right) = 1.53~\textrm{V}
\end{equation*}
12.
01101100
Solution.
\begin{equation*}
V_{out} = V_{ref} \left(\frac{\textrm{value}}{2^n}\right) = 2.56~\textrm{V} \left(\frac{108}{2^8}\right) = 1.08~\textrm{V}
\end{equation*}
