1. Practical Assignment 1 - Combinatorial Logic

Please note that this is the practical component of Assignment 1 - There is a theory part to the assignment too. Please submit these as two separate documents to the CT2 Assignment 1 dropbox in Loop.

Objectives:

To test the operation of basic digital gates: AND, OR, NOT, NAND, NOR.

To test some fundamental laws of Boolean Algebra.

To test De Morgan's Theorem(s).

Use Karnaugh Maps to minimise and implement an expression.

Equipment Required:

The equipment you will require is as follows:

- Your personal logbook (to help you capture your assignment write-up). As you only have one breadboard, remember to take photos/video at each stage of the experiment before you move on and disassemble any part of the experiment.
- Your electronics kit, breadboard and hook-up wire.
- Digital multimeter.

Procedure:

This assignment allows you to gain practical experience of the operation of basic logic gates, both in isolation and in combination to realize more complex boolean functions ("combinatorial logic").

The AND Gate

- Connect one of the 2-input AND gates (74LS08) as shown in Figure 1. Connect two of the digital switches to the A and B inputs of the gate. Connect the output to one of the LEDs, and also to the voltmeter. (If you like, connect the inputs to LEDs also, so that you can verify what signals you are sending in.) Remember to connect power to the Vcc and GND terminals of the IC. Remember to leave the power supply turned off until you are sure that your circuit is wired correctly.

Figure 1: The 2-input AND gate.

- Copy the outline truth table below into your logbook. Vary the inputs A and B (i.e. 0 and +5V) to obtain all the possible combinations and complete the truth table. Enter both the logical value of the output (0 or 1) and the actual voltage (measured using a Digital Voltmeter). Give the exact voltages that you obtained for each state of the gate. Note that, in TTL logic, any voltage above 2.4V is generally classified as logic 1, and any voltage below 0.8V is generally classified as logic 0.

- The 2-input AND gate can be extended to a 4-input AND gate as shown in Figure 2. Connect the gates as shown and generate the values for the truth table below (do not record the actual voltages, just the state).

Figure 2: A 4-input AND gate, built using 2-input AND gates.

Other basic gates

For each of the other basic gates (2-input OR, 1-input NOT, 2-input NAND and 2-input NOR) determine the truth table experimentally (recording them - including the actual voltage output in each case). State whether each one is as you expected. Please note that the 2-input NOR gate has a different pin layout than the OR, AND and NAND gates (see the bottom of this page).

Don't forget to disconnect the power each time you are breaking down or setting up a new circuit and to photograph it!

Disconnected (Open Circuit) Inputs

Pick one of the 2-input gates. Experimentally test its behaviour when either or both of the inputs is left open circuit (unconnected). Describe what you observe in your logbook.

Testing the Associative Law (for AND)

- Connect AND gates as shown in Figure 3 to implement the Boolean equations F=A.(B.C) and G=(A.B).C.

Figure 3: Testing the Associative Law.

- Copy the outline truth table below into your logbook. Before doing any experiments, fill in the column marked P with your predicted outputs (There is only one column for P as F and G should be the same). Now test this experimentally by varying inputs A, B and C to obtain all of the possible combinations, and filling in the measured values of F and G. Comment on whether the results are as you expected.

Testing the Distributive Law

To test the Distributive law, connect AND, OR gates as shown in Figure 4. Draw an outline truth table into your logbook, with columns for A, B, C, P, F and G. Before doing any experiments, fill in the column marked P with your predicted outputs. Now test this experimentally by varying inputs A, B and C to obtain all of the possible combinations, and filling in the measured values of F and G. Comment on whether the results are as you expected.

Figure 4: Testing the Distributive Law.

Testing De Morgan's Theorem(s)

- Connect inputs A and B and their complements /A and /B to AND and OR gates as shown in Figure 5. You will have to use NOT gates (inverters) to obtain the necessary complemented or inverted signals.

Figure 5: Testing De Morgan's Theorem. Note: to achieve /A and /B in the second figure you will need to place two NOT gates on the input side of the OR gate.

- In your logbook, present the Boolean logic equations for F and G. Before doing any experiments, draw a truth table showing your predicted values for F and G. Are F and G equal? Should they be?
- Redraw the truth table, but now measure the actual values of F and G for all possible values of A and B, and fill these into the table. Comment on how these results compare with your predicted truth table.
- Consider the Boolean function F = /(A.(/(A./B)). Draw an outline truth table in your logbook, with columns for A, B, P, and F. Fill in column P with your predicted values for the function. Now devise a circuit to implement the function. Measure the actual values of the output and fill them in, in column F. Comment on whether the results are as you predicted.

The power of NAND

Devise a circuit, using only two NAND gates, that implements a 2-input AND function. Sketch the circuit in your logbook. Build and test the circuit. Record the results in your logbook. Comment on whether they are as you expected.

Minimising an Expression using Karnaugh Maps

The Problem: An industrial process to burn toxic waste has three independent sensors to determine if the flame is lit before waste is injected into the system. It also has an emergency stop button. Because of the nature of the waste, it is important that it is only injected if the flame is lit and the emergency stop button is not pressed. Due to the hostile environment that the sensors are in, one of the sensors routinely fails. The safety regulations allow the waste to be injected if at least two of the sensors detect a flame present and the emergency stop button is not pressed.

Draw a truth table for this system.
- Derive using a Karnaugh Map a minimal sum-of-products function for this system.
- Implement the solution using AND/OR/NOT gates. Use four push buttons to represent the sensors and the emergency stop button. Indicate on the output using red and green LEDs whether the waste should be injected or not.
- Using De Morgan's Theorem remove the AND/OR/NOT gates from your circuit and implement the logic of the circuit using ONLY NAND gates. (Remember to take photos/video of the previous step before you disassemble it).