Dale - Computer Science Illuminated 127

Dale - Computer Science Illuminated 127 - kinds of Boolean...

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100 Chapter 4 Gates and Circuits Now let’s represent the processing of this entire circuit using a truth table: Because there are three inputs to this circuit, eight rows are required to describe all possible input combinations. Intermediate columns are used to show the intermediate values (D and E) in the circuit. Finally, let’s express this same circuit using Boolean algebra. A circuit is a collection of interacting gates, so a Boolean expression to represent a circuit is a combination of the appropriate Boolean operations. We just have to put the operations together in the proper form to create a valid Boolean algebra expression. In this circuit, there are two AND expressions. The output of each AND is input to the OR operation. Thus, this circuit is represented by the following Boolean expression (in which the AND operator is assumed): (AB + AC) When we write truth tables it is often better to label columns using these
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Unformatted text preview: kinds of Boolean expressions, rather than arbitrary variables such as D, E, and X. That makes it more clear what each column represents. In fact, we can use Boolean expressions to label our logic diagrams as well, elimi-nating the need for intermediate variables altogether. Now let’s go the other way; let’s take a Boolean expression and draw the corresponding logic diagram and truth table. Consider the following Boolean expression: A(B + C) In this expression, the OR operation is applied to input values B and C. The result of that operation is used as input, along with A, to an AND operation, producing the final result. The corresponding circuit diagram is therefore: A B C B + C A(B + C) A 1 1 1 1 B 1 1 1 1 C 1 1 1 1 D 1 1 E 1 1 X 1 1 1...
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