2. Practical Assignment 2 - Binary Adders & The Diode

Objectives:

• To build and test a 1-bit half-adder

• To build and test a 1-bit full-adder

• To test an integrated (pre-built) 4-bit full-adder

• To study the properties and characteristics of a silicon diode.

Please note that this is the practical component of Assignment 2 - There is a theory part to the assignment too. Please submit these as two separate documents to the CT2 Assignment 2 dropbox in Loop.

Before we begin:

Before beginning the assignment you should watch the video (you can maximise these videos to full screen):

Now, in this video I use and XOR gate (exclusive OR gate), but that is not available to you in this assignment, 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:

7404: Hex Inverter

Procedure:

Firstly - Locate, and copy into your report the truth tables for 1-bit half- and full adders.

The 1-bit Half-adder

• 1. Construct the circuit as shown in Figure 1.

• 1. 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.

     1. Comment in your logbook on whether this is as you expected.

  2. 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: This requires careful planning in order to build it on a single breadboard - keep the ICs close together and use wires of different colours (that have meaning to you) in order to make it easier to find faults in the circuit.

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

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

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

  3. 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 Fully 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 next thing to be careful of is that there are two different 4-bit full adders in circulation. The 74LS83 and the 74HCT283, which have slightly different pin layouts - be careful!

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. 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. 

Figure 3 shows the pinout of the 74LS83/74HCT283, 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 toS4) and the carry output (C4) from the most significant bit.

(a) The 74LS83 - Please check which IC you are using

(b) The 74HCT283 - Please check which IC you are using

Figure 3: The Four Bit Adder 

Note that this diagram does not show power supply connections, but these are still required to make the device operate. Somewhat unusally, the power supply pins are number 5 (+Vcc) and number 12 (GND).

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 logbook.

Now test all these predictions, using a 74LS83/74HCT283. Record the results in your logbook. Comment on whether or not your predictions were satisfied. Remember to capture photographs of your circuit and attach them to your final report.

The Diode

Introduction

After you have completed the previous section and are finished with your breadboard, the next stage is that you are going to examine how a diode works in a bit more detail. It may be possible to build this circuit on the same breadboard as it doesn't take up too much space. We are going to study the properties of a junction diode and we are going to obtain the characteristics of a silicon diode.

Figure 4. A 1N4001 Silicon Diode - The lighter grey line on the diode indicates the direction that it should be placed in the circuit

Figure 5. The symbol of a diode, where the line on figure 4 aligns with the straight line to the right of this symbol

For this part of the assignment we are going to set up the circuit as shown in Figure 6. There is one difficulty with this assignment and it is that you only have one digital multimeter (DMM). If you had two then the experiment would be a lot less cumbersome - so, if you can borrow a multimeter from someone or pair up with another student in the class then I would recommend it for this part of the assignment. If you cannot then you can still do the assignment, but it will take longer and I can only apologise in advance!

Figure 6. The setup we are using for this part of the assignment

What we are trying to achieve in this part of the assignment is to demonstrate that a diode exhibits a behaviour as described by Figure 7. This graph illustrates that when a diode is forward-biased it allows current to pass freely once we achieve a fairly low 'knee-voltage'; however, when the diode is reverse-biased it does not allow current (negative current) to flow until we reach a fairly high 'breakdown-voltage'. The breakdown-voltage for a diode like this is typically from 50V to 1,000V. In effect, a diode only allows current to flow in one direction (like a one-way water valve). This property means that it can be used to design circuits such as AC to DC converters.

Figure 7. The Volt/Ampere Characteristics of a typical diode.

As well as having only one multimeter, we also have another problem - we don't have a variable voltage supply... so, we'll have to build one before we get started. The easiest way to do this is with a voltage divider, where one of the resistors is a variable resistor (potentiometer). The potentiometer is a 3-legged device in your kit and should have the upper resistance level marked on the side.  

                         (a)                                           (b)                                  (c)

Figure 8. (a) An example of the internals of a potentiometer. You can see that the W pin is connected to the wiper that turns with the dial over the resistive material. The A and B pins are connected at either end of the material, meaning that when the wiper is turned fully to the left that the resistance between W and A is at the minimum, but the resistance between W and B is at the maximum. (b) shows some different styles of potentiometer, and (c) illustrates the voltage divider configuration that should be used in this assignment.

On the forward current side, we need small voltages rather than large voltages, so the configuration that is illustrated in Figure 8(c) should work fairly okay. You should be able to improve the performance to achieve a greater range of lower voltage values by choosing a better value of fixed value resistor. Please describe this in your write-up.

Figure 9. One example setup for the test circuit

Diode Procedure:

- Set up your voltage divider circuit using your 9V battery (i.e. you don't have to use the 5V voltage regulator). The upper voltage will depend on how new your battery is. When it is brand new you will get just over 9V, but as time goes on it will fall to around 5V. Measure the resistance of your potentiometer when it is turned completely clockwise and then anticlockwise. Also, measure the output voltage (Vout) range that you get when this circuit is not connected to the circuit. As discussed, try different resistors to see if you can achieve a better voltage output range at the lower levels (e.g. 0V to 2V). Record these values and describe your procedure in your write-up.

- Now add in the diode and 1k ohm resistor into your circuit as shown in Figure 9. In this configuration the diode is forward biased. Set the potentiometer to its lowest possible voltage output - measure the current through and the voltage across the diode. Change the potentiometer a little and measure both values again. Do this repeatedly about 10 times (take about 5 values between 0.1V and 1V and about 5 between 1V and your highest voltage value e.g. 9V). Record these voltage/current value pairs in your write-up. 

Please note: When you are measuring voltage on the Tenma DMM, set the dial to 2000m/20V and put the red probe in the V Ohm mA slot and the black probe in COM. When measuring current keep the probe locations the same but change the range to 2000uA/20mA.

- Now reverse the direction of the diode in the circuit to measure the reverse-bias characteristics of the diode. With the 1N4001 you will not reach the reverse-breakdown region of the diode. However, please record around 10 values of reverse current and voltage (remember that these will be plotted as -ve current and -ve voltage values)

- Plot a figure like Figure 7. for your diode that includes the forward and reverse biased figures that you have recorded. Estimate the knee-voltage or turn-on voltage for this silicon diode.

Figure 10. Changing the configuration to use an LED instead of the 1N4001 diode

- Replace the diode in your circuit with different LEDs (See Figure 10). You should change the resistor to a more appropriate value for your LED as you will have seen in previous experiments (approx. 100-150 Ohm). Be very careful to put the LED in the circuit in the correct direction to forward-bias it, as they are very easily damaged in reverse breakdown. Find and record the 'turn-on' or knee voltage for each type of LED (e.g. red, green, blue). Why do you think it is different for different LEDs? Record these values and describe your procedure in your write up.

Conclusions

• • State briefly, but clearly, what you have learned from this assignment.

  • What was the most difficult aspect of the assignment?

  • State one thing you enjoyed about the assignment.

  • State one thing you disliked about the assignment.

  • Add any final comment of your own.