Create a truth table for the following conditions and design a corresponding logic circuit: A security system is triggered if: 1. The motion sensor is active AND the door is open.... Create a truth table for the following conditions and design a corresponding logic circuit: A security system is triggered if: 1. The motion sensor is active AND the door is open. 2. The window is broken OR the door is open. From the truth table, derive a simplified Boolean expression, then design the logic circuit.
Understand the Problem
The question asks us to create a truth table based on specified conditions related to a security system. The conditions involve two inputs: a motion sensor and the state of the door, as well as another condition concerning a window. We need to derive a simplified Boolean expression from the truth table and then design a corresponding logic circuit.
Answer
Use conditions: M AND D, W OR D. Simplify with Boolean algebra.
The motion sensor and door opening can be represented as M AND D, and the window broken or door open as W OR D. The truth table will aid in simplifying this to create a logic circuit using Boolean algebra.
Answer for screen readers
The motion sensor and door opening can be represented as M AND D, and the window broken or door open as W OR D. The truth table will aid in simplifying this to create a logic circuit using Boolean algebra.
More Information
By using Boolean algebra, you can derive a simplified expression from the truth table to efficiently design logic circuits with fewer components.
Tips
Ensure all input combinations are covered in the truth table and double-check Boolean simplifications.
Sources
- Activity 2: Security System LogicReal-World - Chegg - chegg.com
- Design a simple logic circuit for a home - Chegg - chegg.com
