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Chapter 9: Problem 65

Write the operation table for the Boolean operation OR.

Short Answer

Expert verified
The OR operation table shows (0,0) -> 0, (0,1) -> 1, (1,0) -> 1, (1,1) -> 1.

Step by step solution

01

Understand the Boolean OR Operation

The Boolean OR operation takes two binary inputs and produces an output. The output is 1 (True) if at least one of the inputs is 1. Otherwise, the output is 0 (False).
02

List Possible Input Pairs

For the Boolean OR operation, the possible binary input pairs are (0,0), (0,1), (1,0), and (1,1). We need to evaluate the OR operation for each of these pairs.
03

Calculate OR Operation for Each Pair

Evaluate the Boolean OR for each pair: - For (0,0), output is 0 OR 0 = 0. - For (0,1), output is 0 OR 1 = 1. - For (1,0), output is 1 OR 0 = 1. - For (1,1), output is 1 OR 1 = 1.
04

Write the Operation Table

Organize the results in a table: | A | B | A OR B | |---|---|--------| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | This table illustrates the result of the OR operation for each pair of inputs.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Boolean OR operation
The Boolean OR operation is a fundamental concept in Boolean Logic. It involves combining two binary inputs to produce a single output. In this operation, the output is true (represented by 1) if at least one of the inputs is true. Otherwise, if both inputs are false (represented by 0), the output is false. This is a crucial operation used in digital electronics and computer science.

The Boolean OR can be summarized as follows:
  • If both inputs are 0, the output is 0.
  • If either input is 1, the output is 1.
In practice, this means whenever you apply the OR operation, you are checking if any of the inputs activate the output.
Truth tables
Truth tables are an excellent tool to visualize and understand Boolean operations. They list all possible combinations of binary inputs and their corresponding outputs. This helps in predicting how Boolean expressions behave for any given set of inputs.

For the Boolean OR operation, a truth table with inputs A and B, and output A OR B, will look like this:
  • When A = 0 and B = 0, A OR B = 0.
  • When A = 0 and B = 1, A OR B = 1.
  • When A = 1 and B = 0, A OR B = 1.
  • When A = 1 and B = 1, A OR B = 1.
By laying out these combinations, truth tables make it possible to see the logical outcome of different binary operations at a glance.
Binary inputs
In Boolean Logic, binary inputs refer to the use of two unique states or values, typically 0 and 1. These are the building blocks of binary systems, which computers and digital circuits utilize extensively. Each input in these systems is easily represented by these two states - false (0) or true (1).

When discussing operations like the Boolean OR, the term "binary inputs" highlights that only two input values are considered at any time, and any logic gate or operation will work based on these values.
  • "0" represents off, no, or false.
  • "1" represents on, yes, or true.
Understanding binary inputs is essential, as they are the foundation for constructing logical expressions and complex computational instructions.

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