CS 245 Combinational Logic Design

Purpose:

1. Successfully reduce a Boolean logic equation to its simplest form.

2. Realize the simplified equation using SSI logic devices.

3. Verify that the circuit correctly implements the truth table of the original equation.

4. Convert a circuit made with AND, OR and NOT gates into one with only NAND gates.

5. Become acquainted with a computer-aided design (CAD) software tool.

Procedure:

Fully reduce the following equation:

X = A'B'C'D' + A'B'C'D + A'B'C D' + A'B C'D' + A'B C'D

+ A B'C'D' + A B'C'D + A B'C D' + A B C'D' + A B C'D

Design a circuit to implement the reduced Boolean equation using AND, OR, and NOT gates.  

Use Circuitmaker or Digital Works to create and simulate the circuit.  Verify that the simplified circuit's truth table matches that of the original logic equation.  (CircuitMaker has online help.  Digital Works also has full online and context sensitive help.  However, you may want to read Getting Started with Digital Works by Dan Stanzione.)

Now, implement the same truth table using only NAND gates. Verify that your NAND gate circuit does indeed reproduce the original truth table.

Questions:

How many IC's, gates, and wires would have been necessary to implement the original logic equation? How many are required for the reduced equation?  (Note: The 7400 IC has 4 2-input NAND gates, 7404 IC has 6 NOT gates, 7408 IC has 4 2-input AND gates, 7432 IC has 4 2-input OR gates.)

What advantages, besides a lower purchase price for the components, are realized by reducing the complexity of the logic circuit?

How does the "cost" (use relative terms -- not absolute dollars) of the NAND circuit compare to that of the AND-OR-NOT circuit? (Note: "Cost" includes PCB size, number of holes and traces on PCB, assembly time, reliability, parts inventory, power usage, etc.)