Laboratory Session 2 - Binary Adders

Objectives:

Equipment Required:

The equipment you require is as follows:

  • Your lab notebook
  • Your Electronics Kit 
  • Your breadboard
  • Your Digital Multimeter

There is no template document for this laboratory as you have seen what is required in the last two laboratories. 

Please submit your laboratory write up to: http://moodle.dcu.ie/mod/assign/view.php?id=27689

The Laboratory

Before the lab begins:


Before the laboratory begins you need to watch the video:

Half Adders and Full Adders


Now, in this video I use and XOR gate (exclusive OR gate), but that is not available to you in this lab, rather you must build the circuit using NAND gates, which is more representative of a real-world half/full adder. Check the notes to see the equivalent circuit for an XOR gate and think about how this could be implemented using NAND gates only.

Useful IC(Chip) Diagrams:


7400 pinout diagram

7400: Quad 2-input NAND


7404 pinout diagram

7404: Hex Inverter


Procedure:

The 1-bit Half-adder

  1. Construct the circuit as shown in Figure 1 using 7400 NAND Gates.


    1-bit Half-adder Logic Diagram

    Figure 1: A 1-bit Half-adder circuit using NAND gates

  2. Vary the inputs A and B (i.e., 0 and +5V) to obtain all the possible combinations and complete a truth table for the sum output S and the carry output C. You should wire up LEDs on your output for S and C to make this step more straightforward.

    Comment in your report on whether this is as you expected.

  3. Could we combine multiple half-adders to implement arbitrary width (n-bit) addition operations? Explain your answer in your logbook.

The 1-bit Full-adder

  1. Build on your previous circuit to create the circuit as shown in Figure 2. Note: You may need to build this over two breadboards. Also, keep your wires colour coded correctly to make it easier to find faults in the circuit. There will be a lot of wires!


    Full Adder Logic Diagram

    Figure 2: A 1-bit Full-Adder circuit using NAND gates

  2. Vary inputs A(k), B(k) and C(k-1) and complete a Truth table for the circuit.

  3. What does C(k-1) represent? What does C(k) represent?

  4. What do you predict would be the outputs of the full-adder if the inputs were all left floating (i.e., not connected)? Test your prediction, and comment on the result.

The Integrated 4-bit Full-adder

There is a second video on the use of a 4-bit Full-Adder, please watch it to help you understand the concept (Please note the video uses a 74HCT283 IC):

The 4-bit Full Adder



In the video I used DIP switches, but this is not necessary for you implementation. Instead, just move the input wires between the high (+5V) and GND voltage rails or wire up simple buttons using a button and a pull-up/pull-down resistor. This is slightly more manual but is fine for this assignment. Just remember that a floating wire (a wire left disconnected) is not necessarily the same as a wire that is connected to GND (You saw this in the first laboratory)

Figure 3 shows the pinout of the 74HCT283, which is an integrated high speed 4-bit Full-adder. It accepts two 4-bit words (A1 to A4) and (B1 to B4) and a carry input (C0). It generates the binary sum outputs (S1 to S4 These are sigma on the chip) and the carry output (C4) from the most significant bit. The carry input (C0) is there to allow you to connect two 4-bit adders together to create a 8-bit adder. For the moment, you can connect this input to GND. Be careful, it you leave it disconnected it will probably be received as a 1.

Use 5 LEDS (4 for the sum and 1 for the carry) on the output side of the adder. Remember to use appropriate resistors (use 100 ohm if in doubt) to limit the current through the LEDs.


Figure 3: The 74HCT283 Four Bit Adder 


Make sure that you know the order of your bits from MSB to LSB. So for the Sum outputs S4 should be your MSB and S1 should be your LSB - but also remember that A4 is your MSB and A0 is your LSB when you are inputting a value.

Consider the following 4-bit binary additions:

  1. 0110 + 0101
  2. 1011 + 0011
  3. 1110 + 0100
  4. 1111 + 1111

For each expression, predict what the sum bits and the carry-out bit should be, both for the case that the carry-in bit is 0 and that it is 1. Record your predictions in your write-up.

Now test all these predictions, using a 74HCT283. Record the results in your write-up. Comment on whether or not your predictions were satisfied.

Conclusions:

  1. State briefly, but clearly, what you have learned from this session.
  2. What was the most difficult aspect of the lab?
  3. State one thing you enjoyed about the session.
  4. State one thing you disliked about the session.
  5. Add any final comment of your own.


There is no template document for this laboratory as you have seen what is required in the last two laboratories. 

Please submit your laboratory write up to: http://moodle.dcu.ie/mod/assign/view.php?id=27689

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