CSC 480 Lab #3

"XOR-scuse me" Lab

Purpose

Become familiar with and use the exclusive-or (XOR) gate to solve logic design problems

Components used

7400 quad 2-input NAND
7486 quad 2-input XOR

Pin layouts for these chips are attached.

Deliverables

For each lab problem, the following items are required:
A brief summary of the problem you are solving
A truth table (or SOP/POS form if appropriate) of the circuit that you are building
A logic diagram of the circuit that you are building... please use your templates!

These items should be added to your report, as needed:
Show the steps (if any) you took to minimize or derive your circuit, such as: K-Maps, Boolean algebra, DeMorgan's Theorem, Consensus Theorem, etc.
Show your instructor (Bill) your circuit, if it's specified that you do so in the problem. There will always be at least one problem that requires inspection during a lab period.

Lab Procedure

From our last lab, I think we can improve our performance by:

  1. Keep your input and output ordering consistent and logical. Label your circuit diagrams using the S1-SN input switches and the L1-LN output lights that you are using.
  2. You only need to assign LED's (lights) to your inputs if you are debugging or having some problem with your circuit. Otherwise, the switch value (and prim/proper ordering of your inputs per the step above) should be sufficient.
  3. Most of the "my circuit isn't working" problems that we had last time were related to chips not being correctly/completely inserted into the breadboard. Take extra care when inserting your chips.
  4. And again, for your safety... unplug the logic box while you are working on it!

Lab Problems

This lab focuses on the design of logic using XOR gates... from page 71, Section 2-7 in our text. Please complete each of the following parts:

  1. Please try the following special cases with 2-input XOR gates:
    Tie one of the inputs of the XOR gate to logic '1' and exercise the other input
    Tie one of the inputs to logic '0' and exercise the other input
    Tie the inputs together (both inputs the same value)

    For each special case, show the truth table, circuit diagram and comment on what common Boolean operation each case mimics.

  2. What function is created when taking the dual of a 2-input XOR Boolean operation? Implement your result with only 2-input XOR gates. Show the Boolean gymnastics you needed to do this. What is the relationship of this circuit to a plain, old 2-input XOR?

    Note: The final two steps aren't hard, rather a bit tricky... XORs "bend" many of our beloved logic design tools, namely Boolean algebra and K-Maps. You will have to recognize the XOR "pattern" with either your equation (A'B + AB') or K-Map (the checker-board pattern) during simplification. The next two problems exhibit these patterns.

  3. Construct a 3-input XOR gate with 2-input XOR gates. Show the Boolean algebra work to justify your design. The trick: you can substitute the XOR operator any time you see the pattern (A'B + AB').
  4. Construct a full adder circuit using 2-input XOR gates and 2-input NAND gates. Show the K-Map for each output to justify your design. Finally, please personally show me your solution in its full glory.

    Note: The full adder is discussed in our textbook on page 126; the truth table appears there. You can also get some solid hints on your design from there.