Simplification of Boolean Functions

Simplification of Boolean Functions - Simplification of...

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Simplification of Boolean Functions Experiment 3 Objective To demonstrate the relationship between Boolean functions and the corresponding logic diagram. Procedure Logic Diagram For this part of the experiment we are given a logic diagram that we must simplify and reduce the number of gates, and possibly the number of ICs. The logic diagram (Figure 3.1) is shown below and requires two ICs – a 7400 and a 7410. Pin numbers were assigned to all inputs and outputs of the gates. We then connected the circuits with the x, y, and z inputs going to three switches and the output F to an indicator lamp. We tested the circuit to obtain the truth table below (Table 3.1). Figure 3.1
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Table 3.1 x y z F 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 Once we had the truth table we were able to create a map to simplify the function F 1 to get F 2 . The map is shown below (Map 3.1) Map 3.1 x yz 00 01 11 10 0 0 0 1 0 1 1 1 1 0 Using this map we determined that F 2 = xy` + yz. Using DeMorgan’s Theorem we converted this function to
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Simplification of Boolean Functions - Simplification of...

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