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Combinational Logic
Electronics Workbench Circuit Simulation using MultiSIM

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:

  1. Double-click on the icon to obtain the detailed logic converter.

  2. Under Conversions click on the circuit-to-truth table button:

  3. 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:

  1. Enter the SOP expression ABCD' + ABEF in the logic converter display.

  2. 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).

MultiSIM Exercises

  1. Connect a 4-input AND gate (7421) to the logic converter icon and convert it to a Boolean expression.
  2. 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.
  3. 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?
  4. 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?

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