lab 3

ELEC201 Digital Electronics

Page 1 of 6

Excelsior College

Module 2: Laboratory 2: Combinational Logic Circuit Design

Objectives

The objectives of this experiment are to:

• Examine the relationship between a Boolean expression and a combinational logic circuit.

• Convert Boolean equations into combinational logic circuits. • Determine the function of a combinational logic circuit.

Introduction

A combinational logic circuit consists of several logic gates connected in such a way that multiple digital inputs are reduced to one or more (in general, fewer) outputs. In this experiment we will examine several combinational logic circuits and their operation.

Procedure

1. Load the circuit E4-1.MS7, shown in Figure 4.1.

Figure 4.1: Simple combinational logic circuit

2. Determine the truth table for the circuit by simulation. To do this, add 0/1 switches on the A and B inputs and a logic indicator on the F output.

A B F

0 0

0 1

1 0

1 1

Table 4.1: Truth table for circuit E4-1.MS7

Module 2: Laboratory2: Combinational Logic Circuit Design

Page 2 of 6

3. Open the Logic Converter ( ). When minimized, it looks like Figure 4.2(a). Figure 4.2(b) shows the actual instrument and its controls.

Figure 4.2(a): Logic Converter minimized icon

Figure 4.2(b): Logic converter details

The Logic Converter allows you to enter a truth table and generate its associated Boolean expression and/or combinational logic circuit. To begin, left-click inside the circles under A and B at the top of the Logic Converter. Its display should look like Figure 4.3 when you have done this.

Module 2: Laboratory2: Combinational Logic Circuit Design

Page 3 of 6

Figure 4.3: Setting up a 2-input truth table

4. Now the 0's and 1’s in the output column must be added. This is accomplished by left-clicking on the? until it becomes the value required (0, 1, or X which means don't care). For our example, enter 1’s on the middle two lines of the truth table and 0's in the first and last lines. Your display should look like Figure 4.4.

Figure 4.4: Truth table ready for conversion

5. The six conversion buttons on the Logic Converter allow you to convert between equations, truth tables, and logic circuits. Clicking the second button from the top displays the Boolean equation for the truth table in the lower display window, as indicated in Figure 4.5.

Module 2: Laboratory2: Combinational Logic Circuit Design

Page 4 of 6

Figure 4.5: Boolean equation for truth table

Notice that the Logic Converter uses a single quote after a variable instead of an overbar to indicate inversion. The equivalent Boolean expression, with overbars, is:

Which is the expanded version of the simpler expression:

6. Left-clicking the second-to-last button converts the Boolean equation into an actual combinational logic circuit, as indicated in Figure 4.6.

Module 2: Laboratory2: Combinational Logic Circuit Design

Page 5 of 6

Figure 4.6: Combinational logic circuit generated by equation

7. Repeat steps 4 through 6 for a truth table containing three inputs (A, B, and C). Ones are required on lines 0, 3, 4, and 5.

8. Repeat step 7 except left-click the third button down (containing SIMP) to simplify the Boolean expression. Are there fewer terms? Is less logic required? Does the circuit operate correctly?

9. The Logic Converter is also capable of determining the truth table (or Boolean equation) for a supplied circuit. Open circuit E4-2.MS7, which indicates the necessary connections (see Figure 4.7).

Figure 4.7: Test circuit for Logic Converter

13. Open the Logic Converter and left-click the first conversion button. Record the truth table determined by the Logic Converter.

A B F

0 0

0 1

1 0

1 1

Table 4.2: Truth table for circuit E4-2.MS7

Discussion

While reviewing your data and results, provide detailed answers to each of the following:

Module 2: Laboratory2: Combinational Logic Circuit Design

Page 6 of 6

1. What basic logic function is being performed by the circuit in step 1 (Figure 4.1)? 2. What is the advantage of simplifying a Boolean equation? 3. What basic logic function is being performed by the circuit in step 9? 4. How is the Logic Converter used to determine the Boolean expression for a

combinational logic circuit?