In this experiment you will learn about designing combinational circuits with discrete parts such as the NAND, NOR, and voltage inverter. In addition, you will go over mixed logic.
For this lab you will need the following parts:
The following is background reading. It may be a review of previous lectures on "mixed logic" and creating circuit diagrams from Boolean expressions.
Note that we have often viewed combinational circuits as "functions" because its outputs (which are voltages) are a direction function of its inputs (which are also voltages). Thus, we can write down its description by a truth table, assuming logic conventions at the inputs and outputs. Another way to describe a combinational circuit is to use a Boolean expression. A Boolean expression has three basic operators (AND, OR, and complement) and two numbers (0 and 1). An example of a Boolean expression is shown in Figure 1.
f(A,B,C) = A'BC + B'C + A
Figure 1. A Boolean expression.
We can convert this Boolean expression (which is a math function) into a circuit diagram (which is a diagram of a physical device) by a four step process.
Step 1. Draw an appropriate logic diagram of the Boolean expression as shown in Figure 2. Notice that the logic symbols have two inputs because we will eventually convert the logic diagram into a circuit diagram. Also remember that a logic diagram still describes a math function, and has nothing to do with anything physical.
Figure 2. The logic diagram for Figure 1.
Step 2. Identify the parts you have, and the kind of logic convention that the inputs an outputs have. Let's suppose you have 2-input NANDs and voltage inverters available, and that the inputs are negative logic while the output is positive logic.
Step 3. Transform the logic diagram into a circuit diagram by replacing logic symbols with circuit symbols (the mixed logic symbols for circuits). Also, indicate the logic conventions of the inputs and outputs by putting a ".L" suffix and a "bubble" at negative logic input/outputs, and putting a ".H" suffix at positive logic input/outputs. The result is shown in Figure 3.
Figure 3 An unfinished circuit diagram
Step 4. In order for the circuit to realize the function in Figure 1, the logic conventions at any connection point has to be the same for inputs/outputs at the point. In other words, the "bubbles" must match. Bubble matching can be done by redrawing the "wire" device so that the bubble is on the other side. As a last resort, voltage inverters can be introduced. The resulting circuit diagram is shown in Figure 4, and we are done.
Figure 4. A correct circuit diagram
You will convert a Boolean expression into a circuit diagram. You will be using the logic switches you built in Lab 3 as inputs, and your logic probes to measure the outputs. You will build and test the circuit, and fill in truth tables and voltage (or function) tables.
Complete each of the following tasks.
Task 1. Draw a logic diagram in LogicWorks for the following Boolean function f(A,B,C) which has inputs A, B, and C.
For the logic symbols, use the EE 260 Logic Library. The library has OR, AND, and complement (or "NOT") symbols. Note that the NOT symbol has an input and output indicated by in and out, respectively. Note that when you draw a logic diagram using LogicWorks, the signals "0" and "1" in the simulator are logic (math) values, i.e., they actually represent the values "0" and "1".
In our LogicWorks logic diagram, attach binary switches to the inputs (A, B, C) and probes to the output (f).
Task 2. Now begin drawing a circuit diagram from the logic diagram.
Task 3. Using your protoboard and a 74'00 chip, you will build this circuit naively (and incorrectly)
Task 5. Re-implement your logic diagram with a circuit diagram using only '02 devices (and '04 devices as needed). Draw the new circuit diagram in LogicWorks, build it on your protoboard and measure the voltage and logic tables for this circuit.
Task 6. Re-implement your logic diagram with a circuit diagram using '00, '02 and a minimum '04 devices as needed. If possible use no voltage inverters ('04). Draw the new circuit diagram in Logicworks, build it on your protoboard and measure the voltage and logic tables for this circuit. Which of these three implementations is better?
For this part of the lab your are to design and build a T flip flop from a D flip flop in the 74'175, '02 and '04 devices.
Task 7. Draw an ASM chart and a state transition table for a T flip flop. Note that you are to implement the T flip flop as a Moore circuit (which is a special case of a Mealy circuit) contrary to what is shown in the figure below. The state register for the Moore circuit is a D flip flop in the 74'175. Derive the truth table for the combinational circuit of the Moore circuit (Note that the truth table has inputs (Q,T) and output D). Write the Boolean expression for D as a function of Q and T.
Task 8. Draw a circuit diagram for the circuit. For the combinational circuit module of the circuit, you may only use '02 and '04 devices. Make sure all bubbles match.
Task 9. With the EE260 Circuit library, you can draw circuit diagrams using LogicWorks. (Remember that a circuit diagram is a diagram of something physical.) The library has mixed logic symbols. Note that the "wire" device has an input and output indicated by in and out, respectively.
Unfortunately the only signals in LogicWorks is "0" and "1". It would have been nice if it could also process the signals "L" and "H" for low and high voltages, but we can't have everything. So remember that in in a circuit diagram in LogicWorks, "0" represents a low voltage, and "1" represents a high voltage (i.e., LogicWorks uses the positive logic convention).
Draw your circuit diagram in LogicWorks using a D-FF and the NOR and "wire" mixed logic symbols from the EE 260 Circuits library. Get a print out of your circuit.
Task 10. Using your protoboard, a 74'02 chip, a 74'04 chip, and a 74'175 chip, build your T flip flop. Show the TA when you have it built.
REMEMBER: The EE 260 Logic library is to be used to build logic diagrams. The EE 260 Circuit library is to be used to build circuit diagrams. Do not mix devices from different libraries, unexpected behavior may result.