CSC 480 Lab #4

"See Jane add... add Jane add" Lab

Purpose

bullet Explore binary addition
bullet Explore binary subtraction using 1's and 2's complement

Components used

bullet 7483 4-bit binary adder

You may need some other little nasties as well. Pin layouts are attached.

Lab Procedure

Last lab went well. Just don't forget the basics:

bullet For your safety... unplug the logic box while you are working on it.
bullet For the health and safety of your chips... use your tongs and watch your power and ground connections.

Lab Problems

This lab focuses on binary addition and subtraction... this stuff is covered on pages 201-221 in our text if you are looking for guidance. Please complete each of the following parts:

1. Unsigned Binary addition

Hookup one of your 7483 binary adders to perform unsigned binary addition.

Connect inputs A and B (4 bits each) to your switches and connect the SUM output (4 bits) and the COUT output to your LED's. What should CIN (or C0) be assigned?

Once you're hooked up, please do the following:

  1. Exercise the A inputs from 0-15, keeping B at 0, and your outputs LED's should count along with you
  2. Do the same thing with your B inputs (count from 0-15), keeping A at 0, and count along on the outputs
  3. Fill in the following table using binary addition:
  A B Cout Sum
  (4 bits) (4 bits) (1 bit) (4 bits)
5+10        
7+6        
1+9        
8+6        
10+10        
15+7        
8+9        
4+15        

2. 1's complementing circuit

Design a circuit that creates the 1's complement of a number. The circuit inputs and outputs should be:

bullet A... 4-bit input value
bullet COMP... a bit controlling whether the number is complemented or not. If 0, then don't complement, otherwise complement.
bullet S... 4-bit output value

Complete a truth table for values 0000-1111, showing the 1's complemented output for each.

3. 2's complementing circuit

Do the same using 2's complement. Hint: You may need some extra hardware to do this one.

4. Adding/Subtracting with 1's complement

Now, let's do some binary addition and subtraction using signed numbers. For problem 2, please use 1's complement to represent negative binary numbers. This means that inputs A and B will now be signed binary numbers in 1's complement form... which implies that the most significant bit is now equal to -(23 - 1) = -7. Your answer, the SUM bits, will also be in 1's complement form.

  1. What changes do you need to make to your current adder setup to perform 1's complement addition/subtraction. Hint: the main difference between 1's complement and unsigned addition is the "end-around carry" operation. Show me how you do this.
  2. You can half-verify that your 1's complement adder/subtractor is okay, by doing repeating the counting exercise from before. Set one input to zero and count from -7 to 7 with the other... your outputs should count along.
  3. Fill in the following table using 1's complement addition/subtraction... please express your answers in 1's complement, except the last column where you check that your answer is correct in decimal form:
  A B Cout Sum Check
  (4 bits) (4 bits) 1 (bit) (4 bits) (decimal)
4+2          
4-2          
2-4          
-4-2          
7-3          
3-7          
3-3          

5. Adding/Subtracting with 2's complement

Basically, repeat problem 2... using 2's complement. Remember that in 2's complement, the most significant bit is -(23) = -8.

  1. Change your wiring to accommodate 2's complement addition/subtraction
  2. Verify your change by counting with each input, from -8 to 7.
  3. Fill in the same table above as you did for 1's complement... using 2's complement representation now.
  A B Cout Sum Check
  (4 bits) (4 bits) 1 (bit) (4 bits) (decimal)
4+2          
4-2          
2-4          
-4-2          
7-3          
3-7          
3-3          

Deliverables

For each lab problem, the following items are required:

bullet A brief summary of the problem you are solving
bullet A truth table (or SOP/POS form if appropriate) of the circuit that you are building
bullet A logic diagram of the circuit that you are building... please use your templates!

These items should be added to your report, as needed:

bullet Show the steps (if any) you took to minimize or derive your circuit, such as: K-Maps, Boolean algebra, DeMorgan's Theorem, Consensus Theorem, etc.
bullet Show me your circuit when it's working.