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Design a logic circuit for a simple automobile door and seat belt buzzer system. Assume that sensors are available to provide digital signals representing the door and seat belt states. Signal $A$ is from the door, where high implies the door is closed; signal $B$ is from the seat belt, where high implies the seat belt is fastened; and signal $C$ indicates whether the ignition switch is turned on. Your circuit should output a signal $X$ that can be used to turn a buzzer on or off, where high implies on. The buzzer should be on if the ignition is on and if the door is open or the seat belt is not fastened. Write out your Boolean expression, draw the logic circuit, construct a truth table, and draw a timing diagram illustrating all functionality.

To design a logic circuit for the automobile door and seat belt buzzer system, we need to create a Boolean expression that represents the conditions for the buzzer to be turned on.

Let's define the following variables:

A: Door state (high = closed)

B: Seat belt state (high = fastened)

C: Ignition state (high = on)

X: Buzzer state (high = on)

The Boolean expression for the buzzer state can be written as follows:

X = (C AND (NOT A OR NOT B))

This expression indicates that the buzzer should be on if the ignition is on and either the door is open or the seat belt is not fastened.

Now, let's draw the logic circuit based on this expression:

Please refer to the solution in this steps.