Question

A security system for a building has three ways of detecting an intruder. 1. Security camera (SC) which sends a 1 when an intruder is detected. 2. Motion sensor (MS) which sends a 0 when an intruder is detected. 3. Noise level detector (NLD) which sends a 1 when the noise level rises beyond a certain threshold. The system should work such that the alarm should sound when • SC doesn’t detect an intruder but the MS and the NLD do • Neither SC nor the MS detects but the NLD does • SC and the MS detect but NLD doesn’t • SC detects only • SC and NLD detect but MS doesn’t However, it has been observed, that when the NLD is off, the system does not sound an alarm even if the SC and MS detect an intruder. Analyze the circuit for the problem and fix it. For the above circuit 1. Construct a Truth table of the current system and analyze, the issue. 2. Construct a Truth Table for the modified (fixed) system.

Answer 1

We will consider three variables S M and N to represent Detected outputs of Security Camera, Motion sensor and Noise level detector respectively. As per the given instruction, the variables will get logical values as given below.

• When security camera detects an intruder, S = 1, else S = 0
• When Motion Sensor detects an intruder, M = 0, else M = 1
• When the noise level rises beyond a certain threshold, N = 1, else N = 0

The system should work such that the alarm should sound when:

• SC doesn’t detect an intruder but the MS and the NLD do. Here S = 0 and M = 0 and N = 1 ($\overline{S}\cdot \overline{M}\cdot N$ = 1)
• Neither SC nor the MS detects but the NLD does. Here S = 0, M = 1, and N = 1 ($\overline{S}\cdot M\cdot N$ = 1)
• SC and the MS detect but NLD doesn’t. Here S = 1, M = 0, and N = 0 ($S\cdot \overline{M}\cdot \overline{N}$ = 1)
• SC detects only. Here S = 1, M = 1, and N = 0 ($S\cdot M\cdot \overline{N}$ = 1)
• SC and NLD detect but MS doesn’t. Here S = 1, M = 1, and N = 1 ($S\cdot M\cdot N$ = 1)

So for either of the above five condition, the output for alarm (A) should be actuvated. So we need to logically OR the different products terms as given below.

$A = \overline{S}\cdot \overline{M}\cdot N+\overline{S}\cdot M\cdot N+S\cdot \overline{M}\cdot \overline{N}+S\cdot M\cdot \overline{N}+S\cdot M\cdot N$

Based on the above expression, we can create a truth table as given below.

But as per the given information, the existing system does not sound an alarm, when noise level detector is off even if security camera and motion sensor detects the intruder. That means when S = 1 and M = 0 and N = 0 the system does not sound the Alarm ($S\cdot \overline{M}\cdot \overline{N}$ = 0). This product term is missing from the Alarm ouput signal (A_e). i.e, the existing system output equation is given by

4e = SMN +SMN+SMN +S.MN

The truth table for the existing system is given below.

Inputs Output Ае S M N 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1

We can combine both truthtable to one as given below

The absence of the term $S\cdot \overline{M}\cdot \overline{N}$ in the existing system is the cause of error. It has been fixed.