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а. AOB= A•B+ A•B b. AOB=(A+B)-(A+B) c. Draw circuits for the right hand side of parts a and b

а. AOB= A•B+ A•B b. AOB=(A+B)-(A+B) c. Draw circuits for the right hand side of parts a and b

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Question

Simplify the following expression using boolean algebra

 

Certainly! Here's how this would appear on an educational website: --- **Boolean Algebra: XOR Operations and Circuit Drawings** **a. Expression 1:** The XOR operation \(A \oplus B\) can be represented as: \[ A \oplus B = \overline{A} \cdot B + A \cdot \overline{B} \] **b. Expression 2:** Alternatively, the XOR operation \(A \oplus B\) can also be expressed using the following equation: \[ A \oplus B = (A + \overline{B}) \cdot (\overline{A} + B) \] **c. Circuit Design Task:** Draw circuits corresponding to the right-hand side expressions of parts a and b to visually illustrate the operations described. **Explanation for Circuit Diagrams:** - **Part a Circuit Design:** - Utilize logic gates to depict the expression \(\overline{A} \cdot B + A \cdot \overline{B}\). - This involves NOT gates to obtain \(\overline{A}\) and \(\overline{B}\), AND gates for both resulting terms, and an OR gate to combine them. - **Part b Circuit Design:** - Construct the circuit for \((A + \overline{B}) \cdot (\overline{A} + B)\). - Implement the OR gates for the operations \(A + \overline{B}\) and \(\overline{A} + B\), followed by an AND gate to complete the expression. Feel free to explore these Boolean expressions by drawing and designing circuits to gain a better understanding of XOR operations in digital logic design. ---
Transcribed Image Text:Certainly! Here's how this would appear on an educational website: --- **Boolean Algebra: XOR Operations and Circuit Drawings** **a. Expression 1:** The XOR operation \(A \oplus B\) can be represented as: \[ A \oplus B = \overline{A} \cdot B + A \cdot \overline{B} \] **b. Expression 2:** Alternatively, the XOR operation \(A \oplus B\) can also be expressed using the following equation: \[ A \oplus B = (A + \overline{B}) \cdot (\overline{A} + B) \] **c. Circuit Design Task:** Draw circuits corresponding to the right-hand side expressions of parts a and b to visually illustrate the operations described. **Explanation for Circuit Diagrams:** - **Part a Circuit Design:** - Utilize logic gates to depict the expression \(\overline{A} \cdot B + A \cdot \overline{B}\). - This involves NOT gates to obtain \(\overline{A}\) and \(\overline{B}\), AND gates for both resulting terms, and an OR gate to combine them. - **Part b Circuit Design:** - Construct the circuit for \((A + \overline{B}) \cdot (\overline{A} + B)\). - Implement the OR gates for the operations \(A + \overline{B}\) and \(\overline{A} + B\), followed by an AND gate to complete the expression. Feel free to explore these Boolean expressions by drawing and designing circuits to gain a better understanding of XOR operations in digital logic design. ---
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