Question $1$:

Design logic function to help control access to the facility based on specific conditions, ensuring security and efficiency. Show the designed logic function along with the truth table of the function.

Scenario: Door Access Control System

Imagine you're designing a door access control system for a secure facility. The system needs to grant access to authorized personnel based on certain conditions. Here's how you can create a logic function for this scenario:

Inputs:

Authorized personnel badge swipe $($A$)($swiped or not swiped$)$

Time of day $($T$)($working hours or non$-$working hours$)$

Door status $($D$)($open or closed$)$

Outputs:

Grant access signal $($G$)($access granted or access denied$)$

Explanation:

The logic function checks whether the authorized personnel badge is swiped AND if it's within the working hours. If both conditions are met, access is granted.

Additionally, if the door is already open during working hours, access is granted without requiring a badge swipe. $($note that if badge is swiped and door is already open but in non$-$working hours, access is denied logically$.)$