Prof. Dr. Thorsten Jungmann (last updated 2026-10-25)
Relates to DET-04 Algorithmic minimization of functions with many inputs and hazard analysis
Task
The output of a combinational logic circuit depends only on its present inputs; a sequential circuit also depends on past inputs and stores information as its state. For each of the following functions, decide whether a combinational logic circuit suffices or whether a sequential circuit is needed, and give a reason.
a) Five functions of a smartphone, as Apple describes them for the iPhone:
- While Low Power Mode is on, the battery icon is yellow.
- Low Power Mode turns off when the battery is charged to 80 % or more.
- A press of the power button (on an iPhone, the side button) wakes the phone; the next press locks it again.
- The phone locks automatically if you don’t touch the screen for a minute or so.
- When the setting System Haptics is off, the phone does not vibrate for incoming calls.
b) Five functions of the heat pump of our example system:
- Its two switching signals of Smart Grid Ready (SG Ready) select one of four operating states.
- During a block by the energy supplier, the heat pump must not start; only frost protection is ensured.
- In the comfort time, a hot-water charging starts when the water falls below 47.5 °C, and it runs until the water has reached about 54 °C.
- The fault list keeps each fault with its number, the heat pump and the date and time.
- The controller counts the defrosting starts of each heat pump: 857 and 843 so far.
c) A short spurious pulse reaches an input of each of these functions. Which of the functions can it change permanently? Explain it with one function from a) and one from b).
Solution
Given
Given explicitly:
- a) five functions of a smartphone, as Apple describes them for the iPhone
- b) five functions of the heat pump of our example system
- c) a short spurious pulse at an input of each function
Known:
- Combinational logic circuit: the output depends only on the present inputs, and a truth table describes it completely; sequential circuit: the output also depends on past inputs, and the circuit stores information as its state (DET-04)
- A short pulse leaves a mark where a sequential circuit takes it in (DET-04)
- Two switching signals of SG Ready select one of four operating states (DET-02)
Required
a) and b) for each function, combinational logic circuit or sequential circuit, with a reason
c) the functions that a short spurious pulse can change permanently, explained with one example from each device
a) Smartphone
A simple test helps: can the same present inputs lead to different outputs? If not, a truth table describes the function, and a combinational logic circuit suffices. If they can, the circuit has to remember something from the past, and a sequential circuit is needed (DET-04, 5.1).
- Combinational logic circuit: whether the battery icon is yellow follows from whether Low Power Mode is on at this moment.
- Sequential circuit: at a battery level of, say, 50 %, Low Power Mode can be on or off, depending on whether you turned it on and whether the battery has been charged to 80 % since. The phone has to store whether the mode is on.
- Sequential circuit: the same input, a press of the power button, has two different effects, depending on whether the phone is locked or awake. The phone has to store this state.
- Sequential circuit: the phone has to know how long ago the last touch was, that is, something about past inputs.
- Combinational logic circuit: the setting at this moment decides whether the phone vibrates; nothing from the past is needed.
b) Heat pump
- Combinational logic circuit: the two signals at this moment fix the operating state; a truth table with four rows describes it completely (DET-02, 6.6).
- Combinational logic circuit: whether the heat pump may start follows from the block and the frost protection at this moment.
- Sequential circuit: at a water temperature of, say, 50 °C, a charging may be running or not, depending on whether it has started below 47.5 °C and not yet reached about 54 °C. The controller has to store whether a charging is running.
- Sequential circuit: the list keeps faults from the past, even when the fault has long gone.
- Sequential circuit: the counter remembers every defrosting start so far; its value depends on everything that has happened before.
c) A short spurious pulse
A combinational logic circuit follows its inputs: if a pulse reaches one of them, the output shows it at most for a moment and returns as soon as the pulse is over. A sequential circuit, in contrast, takes in the pulse and can change its state, and the change remains after the pulse is over (DET-04, 5.2). The pulse can therefore change the functions 2, 3 and 4 of a) and 3, 4 and 5 of b) permanently.
- Smartphone: a pulse at the input of the power button looks like a press. The phone locks or wakes up, and it stays in its new state.
- Heat pump: if the counter counts every pulse at its input as a defrosting start, it counts a start that never happened and shows one start too many from then on.