Objectives

implement a half-adder as a sub-circuit 
implement a full adder using two half adders 
implement a half subtractor as a subcircuit
use a half-adder to create a half-subtractors
use the full adders to implement a 4-bit parallel adder 

Preparation

Read the lab notes 
  
Watch this Adders and Subtractors Tutorial

Lab Assignments

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

   • The "Half Adder" circuit
   • The HalfAdder device/sub-circuit testing circuit
   • Boolean functions for Sum and Carry

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 c_i+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

   • The full adder circuit using two "Half Adder" devices and one additional OR gate
   • Boolean functions for Sum and Carry for the full adder

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

   • The the "Half Subtractor " Circuit.
   • Boolean functions for borrow (b) and difference (d)

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

   • The half subtractor circuit using the "Half Adder" device and two NOT 's
   • Boolean functions for Difference and Borrow (will be slightly different from 3, because of inverters--consider what is going into the box and what is coming out of the box)

5. 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

   • The 4-bit Parallel Adder Circuit using "Full Adder " devices/sub-circuits with the above two examples and another one of your choice.
     Inputs are provided with the one bit input devices. and the outputs will be displayed with the one bit output devices.
   
   
   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.