3. You are hired to design a system that can be used in a safety push button lock device. There will be three buttons, for example, A, B, and C. If an odd number of inputs is pressed, the lock mechanism opens. In any other case, the lock mechanism remains closed. If any two buttons are pressed simultaneously, an alarm sounds. Let's say X is the lock mechanism and Y is the alarm that makes the sound.
i) Construct a truth table for the system.
ii) Find the minimized output expression using Boolean algebra or K-map.
iii) Draw the logic diagram for the system.
14. In a departmental store, you are hired to design a cash register operated by four personnel - the store manager (A), the assistant manager (B), the cashier (C), and the chief accountant (D). At least two of these personnel must be present, along with the cashier, for the register to unlock. Design a logic system that can perform this operation. For your design, show the truth table, write the simplified output expression, and draw a logic diagram.
i) Construct a truth table for the system.
ii) Find the minimized output expression using Boolean algebra or K-map.
iii) Draw the logic diagram for the system.