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Laboratory Session 1 - Combinational Logic

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) - which we will see in later lectures.

    • Equipment Required:

    The equipment you will require is as follows:

    • A lab notebook - not hard-backed, just for keeping records
    • Your electronics kit - borrowed from the Technical Staff through the library loan of a laminated sheet.
    • Digital voltmeter (available at the workstations or with your kit).
    • Collect hook-up wire from the demonstrators and  ICs from your kit.

    You should submit your laboratory write-up electronically at: https://loop.dcu.ie/mod/assign/view.php?id=1157950

    There is a template document at: Template Document to help you to write-up this laboratory.

    Remember to turn off your multimeter when not in use as the battery will go flat very quickly.
    Description:


    This session 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").

    You should study the specific instructions below, in full, in advance of the lab session. Note that, in general, this means that you will also have to research and develop your knowledge of relevant prior concepts, specifically logic gates and boolean algebra (otherwise the instructions below will simply not make any sense...).

    You might find it useful to watch this video in advance of the laboratory session:

    YouTube Video


    Procedure:

    At the start of the lab session:

    • Self-organise into groups of two at each workstation.
    • On a new page in the notebook, fill in an appropriate heading for the lab session, e.g.:
      • Digital Electronics: Lab Session 1
      • Basic Combinatorial Logic
      • Date: 24 Oct 2013
      • Partner Name: Sheldon Cooper

    The AND Gate

    • Connect one of the 2-input AND gates (74HC08) as shown in Figure 1. Connect two wires to the A and B inputs of the gate (Pins 1 and 2) and connect these to the 5V rail. Connect the output (Pin 3) to one of the LEDs via a 100 Ohm resistor as illustrated in Figure 1. Remember to connect power to the Vcc and GND terminals of the IC (Pins 14 and 7 respectively). Remember to leave the power supply turned off until you are sure that your circuit is wired correctly. Use the bench supply to give you a 5V fixed supply. Connect some hook-up wires to leads using crocodile clips and plug them into the DC 5V fixed inputs on the bottom right of the bench supply.

    Figure 1: The 2-input AND gate starting configuration.

    • Copy the outline truth table below into your logbook. Change 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 - Measure voltage across the resistor and the diode to get the actual voltage drop between pin 3 and GND. Your multimeter should be set to measure DC voltage (not the ~ AC voltage setting) in the range of 20V (describes the maximum voltage), so rotate the dial on the multimeter until it is in the DC 20V range. 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. Most of our ICs are either TTL or CMOS.
    A B F V (actual voltage)
    0 0

    0 1

    1 0

    1 1


    • 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.


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



    A B C D F
    0 0 0 0
    0 0 0 1
    0 0 1 0
    0 0 1 1
    0 1 0 0
    0 1 0 1
    0 1 1 0
    0 1 1 1
    1 0 0 0
    1 0 0 1
    1 0 1 0
    1 0 1 1
    1 1 0 0
    1 1 0 1
    1 1 1 0
    1 1 1 1

    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 in your logbook - including the actual voltage output in each case). State whether each one is as you expected. (Do *not* build a 4-input version like in the last section)

    Don't forget to switch off the power supply each time you are breaking down or setting up a new circuit!

    The power of NAND

    Devise a circuit, using only 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.

    Disconnected/Floating (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. 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.
      A B C Predict F Predict GF G
      0 0 0
      		 
      0 0 1
      		 
      0 1 0
      		 
      0 1 1
      		 
      1 0 0
      		 
      1 0 1
      		 
      1 1 0
      		 
      1 1 1
      		 

    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. 

    Boolean Equations

    Consider the logic statement: "If Mary obtains permission from her mother or her father and if Joe or Tom pick her up, she may go to the cinema". This statement may be expressed as a Boolean equation using the following Boolean variables:

    • F = Mary will go to the cinema (true/false)
    • A = Her mother will give her permission (true/false)
    • B = Her father will give her permission (true/false)
    • C = Joe will pick her up (true/false)
    • D = Tom will pick her up (true/false)

    Then F = (A+B).(C+D) is the Boolean equation that describes this statement. Draw an outline truth table into your logbook, with columns for A, B, C, D, P, and F. Fill in column P with your predicted outputs. Devise a circuit to implement the function F and sketch it in your logbook. Build the circuit you have sketched, and test its behaviour experimentally. Fill in the measured values of F in your truth table. Comment on whether the results are as you predicted.

    Testing De Morgan's Theorem(s)

    • Connect inputs A and B and their inverse (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, in the bottom figure you should have an inverter on the inputs.

    • In your write-up, 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 write-up, 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.
    • Use De Morgan's Theorem(s) to simplify the boolean function F = /(A.(/(A./B))). Devise a circuit to implement the simplified function. Measure the actual values of the output and fill them in. Comment on whether the results are as you expected.

    Conclusions:

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

    You should submit your laboratory write-up electronically at: http://moodle.dcu.ie/mod/assign/view.php?id=26111

    There is a template document at: Template Document to help you to write-up this laboratory.

    Relevant IC (Chip) Diagrams:



      

    7400: Quad 2-input NAND             7402: Quad 2-input NOR


       



    7404: Hex Inverter/NOT gates            7408: Quad 2-input AND


    7432: Quad 2-input OR


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