In this tutorial, you will continue to use the MultiSIM logic converter that was introduced in the last tutorial to analyze and implement combinational logic circuits. In this tutorial, you will
- Analyze a combinational logic circuit using the logic converter to generate the truth table and Boolean expression
- Convert a Boolean expression to a logic circuit
- Reduce a Boolean expression to its minimal form with the logic converter
- Reduce a combinational logic circuit to its minimal form
Analyzing a Combinational Logic Circuit
The logic converter can be used to produce the truth table or Boolean expression for a logic circuit that is connected to it. In Figure 5-1, the logic circuit from Figure 5-9(a) in the Digital Fundamentals text is connected to the logic generator icon. The steps in producing the truth table and Boolean expression for this circuit are as follows:
- Double-click on the icon to obtain the detailed logic converter.
- Under Conversions click on the circuit-to-truth table button:
- Click on the truth table-to-simplified expression button:
Since this circuit has six input variables, the truth table is 64 rows long. Of these 64 rows, only 16 can be viewed at a time on the logic converter. To see the entire truth table, you must scroll the display. The Boolean expression appearing in the logic converter is ABCD' + ABEF. Note that EWB uses a prime (') rather than an overbar to indicate the complement of a variable. The expression is always displayed in SOP form. As you can see, the displayed expression agrees with the result in the textbook Figure 5-9(a).
Figure 5-1 MultiSIM analysis of a combinational logic circuit.
Creating a Logic Circuit from an SOP Expression
For MultiSIM to generate a circuit from the previous SOP expression ABCD' + ABEF, you must do the following:
- Enter the SOP expression ABCD' + ABEF in the logic converter
- Click on the logic expression-to-gate button:
The circuit shown in Figure 5-2 is produced by MultiSIM. This is actually the
same circuit as Figure 5-9(b) in the textbook
except that MultiSIM uses only 2-input gates. Therefore, the 4-input AND gates
in the text figure are implemented with three 2-input AND gates as shown.
Figure 5-2 MultiSIM circuit generated from the expression ABCD' + ABEF.
Creating a Logic Circuit from a Non-SOP Expression
When you enter a Boolean expression that is not in SOP form, MultiSIM will produce the circuit in accordance with the form of the expression. For example, using the expression AB(CD' + EF) and clicking on the expression-to-circuit button results in the MultiSIM circuit shown in Figure 5-3(a). Notice that this is basically the same as the circuit shown in textbook Figure 5-9(a). The difference is that the 3-input AND gate is replaced with two 2-input AND gates. Click on the expression-to-NAND button and MultiSIM produces the logic circuit shown in Figure 5-3(b), which is the NAND equivalent of the circuit in part (a). Again, the MultiSIM implementation is restricted to 2-input gates.
(a) MultiSIM gate circuit.
(b)MultiSIM NAND circuit.
Figure 5-3 MultiSIM circuit generated from the expression AB(CD' + EF).
- Connect a 4-input AND gate (7421) to the logic converter icon and convert it to a Boolean expression.
- Enter the expression ABCD in the logic converter and convert the expression to a circuit. Notice how this circuit differs from the one in Exercise 1.
- Enter the output expression from Example 5-6 in the Digital Fundamentals textbook and convert it to a logic circuit. Is the resulting circuit identical to the one in Figure 5-15 in the textbook? Is it logically equivalent?
- Use the logic converter to simplify the expression in Exercise 3 and convert it to a simplified circuit. Is this circuit identical to the one in Figure 5-16(b) of the textbook? Is it logically equivalent?