Question

Design of a home Security System

The homeowner wants an alarm to sound (Y=1) if someone breaks into the house

through a door or a window (A=1) or if something is moving around in the house (B=1)

while the occupants are away.

The user should be able to select one of three operating states:

1. Sleeping state (CD=01): the alarm will sound only if the windows or doors are

disturbed.

2. Away state (CD=10): the alarm will sound if the window or doors are disturbed or if

there is motion in the house.

3. Disabled state (CD=00): the alarm will not sound during normal household activity.

a. (10 points) Find the Boolean expression for the logic circuit.

b. (10 points) Construct a truth table of (C, D, C ?D and C ?D). Find the relation

between D and C ?D and the relation between C and C ?D.

c. (10 points) Simplify the Boolean expression based on the relation in b.

d. (10 points) Convert the Boolean expression in c into a Boolean expression that has

only AND and NOT gates.

e. (10 points) Draw the logic circuit for the Boolean expression in part d using only

AND and NOT gates

Answer 1