Problem

To analyze the behavior of combinational logic circuits using deMorgan's theorem, and simulate the behavior with real world integrated circuits.

Prelab

The prelab involves analysis of the following circuit:

1. Using  DeMorgan's Theorem (and others) simplify F(X,Y) for the circuit above.

2. Create a truth table for the expected F(X,Y) for all the combinations of X and Y.

3. Include a column for the observed output of the circuit.

4. Using the datasheet for the 74LS00 (the chip you will be using in the lab) add pin numbers to the gates in the above circuit.

   • The 74LS00 chip is a Quad 2-input NAND Gate. You can view where the inputs and outputs of each gate are in the datasheet.

   • You should have pin assignments for the input and output of all four NAND gates when you are done.

• • As an example:

  • For the first gate, you could assign pins 1 & 2 on the chip to the switches for X & Y. Notice that pins 1 &2 on the chip are inputs to a NAND gate.

  • Then assign pin 3, which is the output of the gate, to whatever pins you assign to the next 2 gates in the centre of the above circuit.

  • Each of the 2 inputs, and each output from the 4 gates above should have a pin assignment.

  • Note that more than one gate connects directly to X or Y and your hardware circuit should reflect that when you build it in the lab.

Procedure

1. Place your 74LS00 chip in the protoboard, across the center break, near the bottom left is a good position for reaching other sections of the Digital Lab.

2. Hook up the 74LS00 using wire as you indicated in part 4 of the prelab.

3. Connect wires from two of the Data Switches for input X and Y to the pins you assigned to the inputs on the 74LS00.

4. Connect a wire from one of the LEDs to the output you assigned to F in the prelab in order to monitor the output F(X,Y).

   • You only need one wire.

5. Connect pin 7 to GND and pin 14 to +5V, be sure that the chip is oriented correctly, and double check your pin assignment.

   • Incorrectly powering the chip may damage it.

6. Fill in the table produced in Section 2 of your prelab for the observed output by using the switches to simulate all inputs.

   • In the down position, the switch acts as a "0". In the up position, the switch acts as a "1".

Conclusions

1. Compare the predicted result to the tested result, were the results as expected?

2. Comment on the hardware implementation of the circuit as compared to simulating it using Logisim.

3. Other comments or observations.