1. A certain 4 input gate called a LEMON gate realizes the function LEMON(A,B,C,D)=BC(A+D).Show a realization of the function f(w,x,y,z)=Σ( 1,6,9,10,11.14,15)EMON(A,B,C,D)=(w,X,y,Z)=∑(0,1,6,9,1(
with only three LEMON gates and one OR gate. (Assume complemented inputs as available). (4 marks)
2. In a university the candidates who satisfy the following criteria will be selected for the science stream:
·75% marks in Maths and 75% marks in Physics or
·75% marks in Maths and 75% marks in Chemistry or
·75% marks in Physics and 75% marks in Chemistry
Write down the truth table for the above function,derive the Boolean expression from the truth table and simplify it, and finally design a two level digital circuit using NAND gates only for the simplified expression. (4 marks)
3. An elevator system in a large building consists of six elevators. Cars 1 through 4 make up the primary system and are activated at all times. To save energy,cars 5 and 6 are completely shut down and are used only when the traffic is heavy. It is necessary to design a logic circuit that monitorsthe four primary cars and generates an "activate"signal when all four cars of primary system are in use. The "activate" signal will cause the remaining two cars to become available for use. In addition,a "standby"signal should be generated for the cars when any three of the primary elevators are in use.A "standby"signal causes the motors of cars 5 and 6 to start, and an "activate" signal allows cars 5 and 6 to be used by the building occupants. Assume that four input lines are available, labelled X, Y,W,and Q, indicating the conditions of the first four cars. A"1”on one of these input lines indicates that a car is is in use, while "0" indicates that a car is idle.
Design a minimal logic circuit that provides the appropriate logic signals to the standby cars.Any type of logic gates may be used. (6 marks)
4. Redesign the following logic circuit expression for the output to make it more efficient (simplified). The output X is equal to
X=PQ.S)PR+P.Q.RS+PQR
(4 marks)
5. An assembly line has 3 failsafe sensors and 1 emergency shutdown switch. The Line should keep moving unless any of the following conditions arise:
o If the emergency switch is pressed.
o If sensor 1 and sensor 2 are activated at the same time.
o If sensor 2 and sensor 3 are activated at the same time.
o If all three sensors are activated at the same time.
a) Derive the truth table for this system (2 marks)
b) Simplify the output using Boolean algebra and draw the minimum (reduced)logic circuit.
