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Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 29EQ
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### Boolean Logic Problem **Question:** Select the Boolean Expression that corresponds to the output of the Boolean process flow below. **Diagram Explanation:** 1. **Inputs:** - There are two inputs, labeled `x` and `y`. 2. **Flow:** - The input `x` is fed into a NOT gate, which inverts its value, creating `x'`. - The input `y` is directly connected to the OR gate and also inverted through a NOT gate to create `y'`. - The first OR gate receives `x'` and `y` as inputs. - The output from this OR gate is connected to the first AND gate. - The input `y` is also fed into another NOT gate, and its output `y'` is an input for the second AND gate. - The two outputs `x'` and `y'` are connected to the second AND gate. - Finally, the outputs of the AND gates feed into another OR gate, providing the final output. **Answer Choices:** - A) \( \overline{x}\overline{y} + \overline{x} + y \) - B) \( (x + z)(y\overline{z}) \) - C) \( xz + \overline{x}y\overline{z} \) - D) \( (x+y)(\overline{x}+y) \) **Correct Expression:** Upon analyzing the circuit, we observe that: 1. The first OR gate performs \( x' + y \). 2. The AND gate then combines \( x' \) with the result of the OR, giving \( x'y \). 3. The final OR operation combines \( x'y \) and another result from a second AND gate, which here is consistent with \( x', y' \) directly to the final OR. The expression that best matches this procedure is likely to depend on the specific combination reflected after reviewing all gates. Calculate according to the full logical path through the circuit to ascertain if A, B, C, or D matches the derived output. In this case, **option D**: \( (x + y)(\overline{x} + y) \) matches the analyzed circuit design.
Transcribed Image Text:### Boolean Logic Problem **Question:** Select the Boolean Expression that corresponds to the output of the Boolean process flow below. **Diagram Explanation:** 1. **Inputs:** - There are two inputs, labeled `x` and `y`. 2. **Flow:** - The input `x` is fed into a NOT gate, which inverts its value, creating `x'`. - The input `y` is directly connected to the OR gate and also inverted through a NOT gate to create `y'`. - The first OR gate receives `x'` and `y` as inputs. - The output from this OR gate is connected to the first AND gate. - The input `y` is also fed into another NOT gate, and its output `y'` is an input for the second AND gate. - The two outputs `x'` and `y'` are connected to the second AND gate. - Finally, the outputs of the AND gates feed into another OR gate, providing the final output. **Answer Choices:** - A) \( \overline{x}\overline{y} + \overline{x} + y \) - B) \( (x + z)(y\overline{z}) \) - C) \( xz + \overline{x}y\overline{z} \) - D) \( (x+y)(\overline{x}+y) \) **Correct Expression:** Upon analyzing the circuit, we observe that: 1. The first OR gate performs \( x' + y \). 2. The AND gate then combines \( x' \) with the result of the OR, giving \( x'y \). 3. The final OR operation combines \( x'y \) and another result from a second AND gate, which here is consistent with \( x', y' \) directly to the final OR. The expression that best matches this procedure is likely to depend on the specific combination reflected after reviewing all gates. Calculate according to the full logical path through the circuit to ascertain if A, B, C, or D matches the derived output. In this case, **option D**: \( (x + y)(\overline{x} + y) \) matches the analyzed circuit design.
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Step 1

A circuit is given 

We have to find boolean expression

Using OR, AND and NOT gate. 

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