CS201 Lab: Design Adders & Subtractors

Objectives

• implement a half-adder as a device
• use this half-adder to create other circuits such as: full-adders and half-subtractors
• implement a half subtractor as a device
• implement a full adder as a device
• use the half subtractor and full adder devices to implement a full subtractor

Preparation

• Read the lab notes

Lab Assignments

1. Following the notes in the lab, you should have completed the half adder device.
   Use the device (the box) and connect binary probes and switches to ensure that the truth table is correct.
   Write the boolean functions for sum and carry beside the circuit
   
   Hand-In

   • The underlining circuit of the "Half Adder" device. (Circuit with labeled ports--Part 1 in the notes)
   • Boolean functions for Sum and Carry
   • The "Half Adder" device (the box) with binary switches and binary probes connected to it

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

   Hand-In

   • Circuit using two "Half Adder" devices and one additional gate
   • Boolean functions for Sum and Carry

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.
   Following the steps from the notes, produce the "Half Subtractor" device.
   Then, use the device and connect binary switches and binary probes to 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 underlining circuit of the "Half Subtractor " device. (Circuit with labeled ports--Part 1 in the notes)
   • Boolean functions for borrow (b) and difference (d)
   • The "Half Subtractor " device (the box) with binary switches and binary probes connected to it

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

   • 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. 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

   • Circuit using two "Half Subtractor" devices and an OR gate
   • Boolean functions for Difference and Borrow

6. Show that a full subtractor can be implemented using a "Full Adder" device and two inverter gates.
   For this, you will have to create a "Full Adder" device (Note: you can use the idea of what you built in question 2)
   Build and test your circuit with the truth table.
   Write the expressions of the difference and the borrow beside the circuit.

   Hand-In

   • The underlining circuit of the "Full Adder " device. (Circuit with labeled ports--Part 1 in the notes)
   • Boolean functions for Difference and Borrow (a little different from question 5 because of the inverters)
   • Circuit using "Full Adder " device and two NOT gates

Summary:

At the end of this exercise, you should have:

• Three devices in a library:
  • "Half Adder"
  • "Half Subtractor"
  • "Full Adder
• Six circuits using the above devices:
  • Half Adder
  • Full Adder Using Half Adders
  • Half Subtractor
  • Half Subtractor Using Half Adder
  • Full Subtractor Using Half Subtractors
  • Full Subtractor Using Full Adder
• Boolean functions written for the outputs of each of the circuits