please can some give me more explanation on this question and explain the truth
ID: 2248931 • Letter: P
Question
please can some give me more explanation on this question and explain the truth table and boolean : Professor X keeps his final exams in his Lab. For security reasons, he would like you to design an alarm system for his Lab. The Lab has a window and door that are equipped with sensors that output a one when they are secured (i.e., closed). When the alarm system is activated with a key, an LED should light up if either the window or door opened. Using three inputs for door, window, and alarm activation and an LED as the output construct appropriate front panel and block diagram in LABVIEW. Create appropriate truth table and Boolean expression before proceeding.
Explanation / Answer
Step1: Referencing Variables
A - Alarm System Activation (0 - Deactivate, 1 - Activate)
D - Door sensor output (1 - Secure, 0 - Breached)
W - Window sensor output (1 - Secure, 0 - Breached)
L - Alarm LED activation status (1 - Activate, 0 - Deactivate).
Step 2: Truth Table
The output is 1 only when Alarm is activated(A=1) and either door or window is open(D or W is 0).
Representing the table in canonical minterms, we get
L = AW'D' + AW'D + AWD'
Where 'denotes complement
Reduction 1 L = AW'(D' + D) +AWD' which simplifies as L = AW'+AWD' by additive identities X'+X=1.
Final equation after reduction 1 is L = A(W'+WD')
Reduction 2 L = A((W'+W).(W'+D'))
by distributive law X+YZ = (X+Y).(X+Z)
Reduction 3 L = A.(W'+D') again by additive identity used in Reduction 1.
So final implementation after reduction is
L = A.(W'+D')
A D W L 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0Related Questions
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