Assignment $1$: Security System Alert Logic

Objective: Determine the logic for a security system's alarm using a truth

table, simplify it with a Karnaugh map, and derive the simplified Boolean

expression.

Scenario: A security system uses three sensors to decide whether to

activate an alarm. The sensors are:

$*$A $=$ Motion Detected $(1=$ yes, $0=$ no$)$

$*$ B $=$ Door Open $(1=$ yes, $0=$ no$)$

$*$ C $=$ Window Broken $(1=$ yes, $0=$ no$)$

The alarm should activate only if motion is detected and either the door is

open, or the window is broken.

Tasks:

$1.$ Create a truth table for the given scenario.

$2.$ Use a Karnaugh map to simplify the Boolean expression based on the

truth table.

$3.$ Derive the simplified Boolean expression for when the alarm should

activate.

Assignment $2$: Temperature Alert System

Objective: Use a truth table and a Karnaugh map to simplify the logic for a

temperature alert system and derive the simplified Boolean expression.

Scenario: A machine is equipped with three temperature sensors to monitor

overheating.

The system must activate an alert if any two sensors report a dangerous

temperature. The sensors are:

$*$A $=$ Sensor $1$ indicates dangerous temperature $(1=$ yes, $0=$ no$)$

$*$ B $=$ Sensor $2$ indicates dangerous temperature $(1=$ yes, $0=$ no$)$

$*$ C $=$ Sensor $3$ indicates dangerous temperature $(1=$ yes, $0=$ no$)$

Tasks:

$1.$ Create a truth table for the alert system based on the conditions given.

$2.$ Use a Karnaugh map to simplify the Boolean expression for when the

alert should be activated.

$3.$ Derive the simplified Boolean expression from the Karnaugh map.