Digital Circuit Analysis and Design with Simulink Modeling and Introduction to CPLDs and FPGAs, Second Edition

7.2: Obtaining Boolean Expressions from Logic Diagrams

7.2 Obtaining Boolean Expressions from Logic Diagrams

When a logic circuit is given, the Boolean expression describing that logic circuit can be obtained by combining the input variables in accordance with the logic gate functions. The procedure is best illustrated with the examples that follow.

Example 7.10

For the logic circuit of Figure 7.19 find D = f(A, B, C), that is, express the output D in terms of the inputs A, B , and C. If possible, simplify the Boolean expression obtained, and implement it with a simplified logic diagram.


Figure 7.19: Logic diagram for Example 7.10

Solution:

We label the output of each gate as shown in Figure 7.20.


Figure 7.20: Outputs of the gates of logic diagram for Example 7.10

From Figure 7.20


The simplified logic diagram is shown in Figure 7.21.


Figure 7.21: Simplified logic diagram for Example 7.10

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