1.1Compute an ADC Step
What is the ideal voltage step of a 10-bit ADC with a $5\ \mathrm V$ reference?
Solution
$$
q=\frac{V_{ref}}{2^N}=\frac{5}{2^{10}}=0.00488\ \mathrm V\approx4.88\ \mathrm{mV}.
$$
Embedded Systems Practice
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1.2Choose a Sampling Rate
A sensor contains useful content up to $100\ \mathrm{Hz}$. What is the minimum ideal sampling-rate condition to avoid aliasing?
Solution
$$
f_s>2f_{max}=2(100)=200\ \mathrm{Hz}.
$$
Practical designs usually sample faster to allow an anti-alias filter transition band and timing margin.
1.3Calculate PWM Average
An ideal $0$-to-$12\ \mathrm V$ PWM signal has duty cycle $25\%$ and drives a sufficiently slow resistive load. What is its average voltage?
Solution
$$
V_{avg}=DV=0.25(12)=3\ \mathrm V.
$$
1.4Find a Timer Period
A timer clock is $1\ \mathrm{MHz}$, the prescaler is $10$, and $ARR=999$. Find the timer period.
Solution
$$
T=\frac{p(ARR+1)}{f_{clk}}=\frac{10(1000)}{1{,}000{,}000}=0.010\ \mathrm s=10\ \mathrm{ms}.
$$
1.5Estimate Task Utilization
A task executes for $0.5\ \mathrm{ms}$ every $5\ \mathrm{ms}$. What is its utilization?
Solution
$$
U=\frac{C}{T}=\frac{0.5}{5}=0.10.
$$
The task uses an estimated $10\%$ of the processor before accounting for interrupts, scheduling overhead, blocking, and other tasks.
1.6Distinguish Volatile from Atomic
Why is declaring a shared variable volatile not enough to make an increment safe between an ISR and foreground code?
Solution
volatile prevents the compiler from assuming that the value is unchanged between accesses. It does not make a read-modify-write increment atomic. The ISR can occur between the read and write, so use an atomic operation, a protected critical section, or a suitable synchronization design.
1.7Select a Protocol Property
Does UART by itself define message boundaries and guarantee that a received message is valid?
Solution
No. UART defines electrical signaling and an asynchronous character frame, but an application must add message framing, length or terminators, timeout rules, and an integrity check such as a checksum or CRC.
1.8Identify a Useful Test
Give one fault-injection test for a temperature controller and state the expected safe response.
Solution
Disconnect or substitute an out-of-range temperature sensor. The firmware should detect the invalid signal, record a diagnostic, and move the heater or actuator to its specified safe state rather than continuing with an untrusted measurement.