An electronic system for bottling tablets is to be designed. The system operators as follows: $$ Tablets are fed from a storage vat, one at a time, into funnel that is fitted with a sensor for counting each tablet as it passes into the bottle. There is a display that shows a running total of the tablets. $$ When a bottle is full, it activates a checking mechanism for comparing the number of tablets in the bottle with the maximum number of tablets that it should have. This number is entered using a keypad. If the numbers are equal, the system resets after $5$ seconds, the flow of tablets ceases, the conveyor belt is activated and the next bottle to be filled moves into position. $$ The total number of tablets bottled at any point in time during a processing period is displayed. As the team charged with designing the system, you are required to provide a prototype that can fill each bottle with $15$ tablets and handle at least $5$ bottles during a processing period. Create the truth table, k$-$map, and logic gate for this scenario