Exercise DET-04.06 – Vibration for an incoming call

Prof. Dr. Thorsten Jungmann (last updated 2026-10-25)

Relates to DET-04 Algorithmic minimization of functions with many inputs and hazard analysis

Task

Your smartphone can vibrate when a call comes in. Two settings decide when: one for silent mode and one for ring mode. On an iPhone, for example, a single setting with four options covers both: Always Play, Play in Silent Mode, Don’t Play in Silent Mode and Never Play. The phone vibrates for an incoming call in silent mode if vibration is switched on for silent mode, and in ring mode if vibration is switched on for ring mode. The inputs and the output are:

• $A$: a call is coming in
• $B$: silent mode is on; otherwise, the phone is in ring mode
• $C$: vibration is switched on for silent mode
• $D$: vibration is switched on for ring mode
• $Y$: the vibration motor runs

a) Set up the truth table of $Y$ with $A$ as the input with the highest weight, and give its minterm list.

b) Minimize $Y$ with the Quine–McCluskey algorithm.

c) While a call is coming in, you switch the phone from silent mode back to ring mode, and vibration is switched on for both modes. Can the output $Y$ of the two-level circuit of your result from b) drop to 0 for a moment? Give a reason with the Karnaugh map.

d) Make the circuit free of this hazard, and draw it according to the standard of the International Electrotechnical Commission (IEC), IEC 60617.

Solution

a) a 1 in rows 9, 11, 14 and 15, a 0 in all other rows; $Y(A,B,C,D)=\sum m(9,11,14,15)$
b) prime implicants $A\cdot B\cdot C$, $A\cdot \overline{B}\cdot D$ and $A\cdot C\cdot D$; essential: $A\cdot B\cdot C$ and $A\cdot \overline{B}\cdot D$; $Y=A\cdot B\cdot C+A\cdot \overline{B}\cdot D$
c) yes: the change of $B$ leads from minterm 15 to minterm 11, two neighbouring ones in the different loops $A\cdot B\cdot C$ and $A\cdot \overline{B}\cdot D$; $Y$ can drop to 0 for a moment, a static 1 hazard
d) $Y=A\cdot B\cdot C+A\cdot \overline{B}\cdot D+A\cdot C\cdot D$: an inverter for $B$, three AND gates with three inputs each and an OR gate with three inputs

▶️ Full worked solution