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Part A (4 Marks)

1)  The above diagram has three distinct logic gates, identify and describe the function of each gate (2 marks).

2) This circuit is equivalent in function to a single gate. Create a truth table for the circuit and from this identify the equivalent logic gate (2 marks).

 

Part B (4 Marks)  

A building has a fire alarm with two switches, A and B, if both switches are open the alarm is inactive, if a switch is closed, regardless of the state of the other switch, the alarm becomes active.

1) Draw a truth table representing all possible states of the switches and alarm (2 marks). e.g.

X Y A open open OFF ... ... ... ... ... ...

 

2) Calculate the Boolean algebra expression for the truth table created in (1). You may use any valid notation presented during the course, as long as you are consistent (1 mark).

A = ?

3) Draw a digital logic gate schematic which implements this logic and name the gate(s) used (1 mark).

 

Part C (4 Marks) Consider this diagram of a full adder.   1) Three gates are missing from the diagram. Identify the gates that should be at spots 1, 2 & 3 (3 marks).
2) A full adder is made by combining 2 half adders. Using your response in (1) draw the complete diagram of a full adder and circle each half adder (1 mark).
  Part D (8 Marks) Consider the following circuit.  

 

1) A student believes that when W=1, Y=0, Z=0, X=1 that the output will be 1. Is this correct? Justify your response (4 marks).   2) Write a boolean expression for the logic circuit, simplifying as appropriate. Justify each step of your simplification. Recall that boolean algebra has several named laws that can be used to simplify expressions such as the distributive law (4 marks).    

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