Given the following logic expression:

F = ABCD + A!BC + AB!C + A!B!CD,

1. Find the minimum expression, using a K-map.

2. Draw and fully label the REDUCED schematic using only 2-input AND (74HC08), 2-input OR (74HC32) and inverter (74HC04) gates.

(end of pre-lab)

Lab Exercise 8: K-MAP Circuit Reduction and Introduction to Stimulus Generator and Logic Analyzer

The purpose of this lab is to demonstrate the usefulness of K-MAPs for combinational logic circuit reduction and to introduce the student to the logic analyzer laboratory equipment.

1. Construct a truth table based on the Boolean equation given in the pre-lab.

2. Draw and fully label a schematic for the Boolean equation given in the prelab. DO NOT use the reduced equation from the K-map! That will be done later in the lab. Include gate identifiers, pin numbers, and chip designators ("U" numbers) on your schematic. YOU DO NOT HAVE TO BUILD THIS CIRCUIT!

3. Build the minimized circuit you designed after performing the K-MAP simplification (from part 2 of the pre-lab). For every high and low combination of the inputs, test your circuit by using a logic probe. Construct a truth table showing your results. This truth table should agree with the truth table you derived from the unsimplified circuit (from part 1). If they do not agree, find out where the problem is before proceeding. When finished, turn the protoboard off, but DO NOT DISASSEMBLE YOUR CIRCUIT YET.

4. You will now hook the logic analyzer to your circuit. Refer to the model setup in the lab when needed.

a. Hook up the counter chip -- V_cc, ground, the clock, and outputs -- as shown in class.

b. When working with digital circuits, it is extremely important to establish a common ground between all parts of the circuit and any instruments acting on the circuit. Otherwise, the circuit simply may not work. On the logic analyzer pod, find a ground lead. Plug it into a pin header that is placed so it is in contact with the ground on your AND gate chip and then run a wire to the ground pin on the counter. A common ground has now been established between the stimulus (the counter), logic analyzer, and circuit.

c. You will now hook the logic analyzer up to the inputs and output of your circuit. It is an unfortunate, but somewhat unavoidable occurrence that the logic analyzer lines tend to break. Whenever this happens, we try to put a tag on the logic analyzer pod indicating which lines do not presently work. Look at the logic analyzer pod for any such note. The following instructions assume your pod is fully functional. If you have a pod where any of the first four lines are not working, do not use these lines, but simply use the next available ones.

Place another pin header alongside the one where A, B, C, and D tie into your circuit so that you will have another set of nodes that tie to those inputs.

From the logic analyzer pod, attach line 1 to signal A on the pin header. Likewise, attach lines 2, 3, and 4 to signals B, C, and D respectively. Having the four input stimuli attached to the logic analyzer will enable you to monitor your A, B, C, and D inputs. Next, attach line 5 from the logic analyzer pod to a pin header that comes into contact with the output ("F") of your circuit.

d. Call one of the lab TA’s over to look over your wiring.

5. Login to a PC (Windows NT network) and load the logic analyzer software (PA485 on the taskbar, under the Programs menu).

a. Double click on the Field Editor icon. A channel number versus signal name chart appears. Wherever there is an asterisk, this means that that particular channel number is mapped to that signal name. For instance, when you first invoked the field editor, "control" was mapped to channels 41 through 48, "databus" was mapped to channels 25 through 40, and "addrbus" was mapped to channels 1 through 24. At this time, click the mouse on each asterisk to make them disappear (and thus destroy the default channel to signal name mapping scheme).

b. Go back to the vertical column where the default signal names are (control, databus, and addrbus). Go to the first field ("control") and activate it with the mouse. Press the delete key to remove "control" and then type an "A" in its place. Similarly, do this to the next four fields and type "B", "C", "D", and "F" in each one, respectively.

c. Across from where you entered the "A" signal name, click the mouse under channel 1 so an asterisk appears. In the same way, across from signal B, click under channel 2. For signal C map channel 3, for signal D, map channel 4, and for the output F, map channel 5.

d. Under the Edit menu, select clock setup. Change the clock mode (sampling rate) to 100 KHz.

e. Click on the Internal Trigger Patterns icon to activate a trigger point. You should see a column for every signal you have defined. Under all your inputs, replace the "x" with a "0" in the pattrn01 row. Leave the output column, F, as an "x". The logic analyzer is now configured to begin data collection when it senses A, B, C, and D to be zeros.

f. Under the File menu, select Save and then Setup Conditions. Save the setup conditions you just configured in a file with a .set extension (for example, lab8.set or 3bit.set).

6. Wire up the counter chip to provide the A, B, C, and D inputs to your circuit, as shown in class.

7. Turn the protoboard on. Go back to the logic analyzer window and click the mouse on the Go button. If everything is working, the logic analyzer should trigger (you should hear a beep when the logic analyzer triggers). If your logic analyzer does not trigger, call for assistance.

If the logic analyzer is working properly, a window with five waveforms for the input and output signals should appear. Remember, you may have to maximize the waveform display from icon form.

If a total of five waveforms do not appear in the waveform editor, be sure to ask for assistance!!

Once the waveforms are visible (and each signal is toggling properly -- no flat liners!), verify the output for each state (from 0000₂ to 1111₂) with the truth table from part 1.

Zoom in or out so that you can read the waveforms easily. Place cursors in the middle of the 0000₂ state (for the red line cursor, use the left mouse button) and the 1111₂ state (for the blue line cursor, use the right mouse button). Zoom out so that the distance between the red and blue cursors takes up only an eighth or so of the window. Print out your waveform data (be sure to select Between Red and Blue Markers so that only the data between the two cursors will print out) and include this in your lab book.