CS201 Lab: Design Adders & Subtractors

Objectives

Preparation

Lab Assignments

Please note:
To make it easier for marking, you are required to submit
one .pdf file and one .circ file, they will contain all the required components for the lab assignment.
This will apply to Lab #1 to Lab #6.

  1. Build the half adder circuit.
    Test the circuit and ensure that the truth table is correct.
    Write the Boolean functions for sum and carry beside the circuit


    Open a new circuit window and test your HalfAdder device/sub-circuit.
    Here is a testing circuit for your reference.


      Hand-In

  2. As mentioned in the notes, a full adder can be designed by using two "Half Adder" devices/sub-circuits and one additional OR gate.
    (Hint ci+1= the sum of the carries out of the two half adders).
    Build and test your Fulladder circuit with the truth table.
    Write the Boolean functions for sum and the carry beside the circuit.

    Hand-In

  3. A half subtractor subtracts two bits, x and y producing their difference d.
    It also has an output b to specify if a 1 has been borrowed from the next higher position.
    The truth table is given below.
    Draw the "Half Subtractor" circuit, then, test the truth table.
    Write the Boolean function for d and b beside the circuit.
    Input
     
    Output
    x
    y
     
    b
    d
    0
    0
     
    0
    0
    0
    1
     
    1
    1
    1
    0
     
    0
    1
    1
    1
     
    0
    0

    Hand-In

  4. Using the property that:

    Show that a half subtractor can be implemented using a "Half Adder" device and two inverter gates.
    Build and test this circuit with the truth table.
    Write the expressions of the difference and the borrow beside the circuit.

    Hand-In

  5. A full subtractor can be built using two "Half Subtractor" devices and an OR gate.
    Design and test a full subtractor (schematic diagram and truth table shown below).
    Write the expressions of the difference and the borrow beside the circuit.
    Input
     
    Output
    x
    y
    bi
     
    bi+1
    d
    0
    0
    0
     
    0
    0
    0
    0
    1
     
    1
    1
    0
    1
    0
     
    1
    1
    0
    1
    1
     
    1
    0
    1
    0
    0
     
    0
    1
    1
    0
    1
     
    0
    0
    1
    1
    0
     
    0
    0
    1
    1
    1
     
    1
    1

    Hand-In

  6. Show that a full subtractor can be implemented using a "Full Adder" device and two inverter gates.
    You have a "Full Adder" circuit n part 2 already.
    Build and test your circuit with the truth table.
    Write the expressions of the difference and the borrow beside the circuit.

    Hand-In

  7. Build a 4-bit parallel adder by using four "Full Adder" devices.
    For this, you will use the "Full Adder" device from your circuit in the previous step.
    Build and test your circuit with the examples:
     
    
    	  0101 
     	+ 0010 
    	-------
    	  ????
    
    
              0110 
    	+ 0011 
    	-------
    	  ????
    
    
              and any other examples of your choice
        

    Hand-In



    Please note:
    To make it easier for marking, you are required to submit
    one .pdf file and one .circ file, they will contain all the required components for the lab assignment.
    This will apply to Lab #1 to Lab #6.

Copyright: Department of Computer Science, University of Regina.