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Logic Function X = (AB+C)(B+C) Logic Diagram with Gates

Logic Function X = (AB+C)(B+C) Logic Diagram with Gates

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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Can you draw a logic diagram with gates for the equation in the photo, please? 

**Logic Function and Diagram Representation** The image presents a logic function and indicates where a logic diagram with gates would be depicted. **Logic Function:** The given logical expression is: \[ X = (AB + \overline{C})(\overline{B} + C) \] **Explanation of the Logic Function:** - \( AB + \overline{C} \): This portion suggests an OR operation between the result of ANDing variables \( A \) and \( B \), and the NOT operation on variable \( C \). - \( \overline{B} + C \): This portion indicates an OR operation between the NOT operation on variable \( B \) and variable \( C \). - The overall expression multiplies (AND operation) the results of the two OR operations mentioned above. **Logic Diagram with Gates:** While the logic diagram is not depicted in the image, based on the expression, it would typically involve: - An AND gate for the entire expression \( X \). - OR gates for each inner part of the expression (\(AB + \overline{C}\) and \(\overline{B} + C\)). - NOT gates for the negations \(\overline{C}\) and \(\overline{B}\). **Purpose in Education:** This structure is used to teach students about constructing logic gates diagrams from Boolean algebra expressions, highlighting the use of AND, OR, and NOT operations in digital circuits design.
Transcribed Image Text:**Logic Function and Diagram Representation** The image presents a logic function and indicates where a logic diagram with gates would be depicted. **Logic Function:** The given logical expression is: \[ X = (AB + \overline{C})(\overline{B} + C) \] **Explanation of the Logic Function:** - \( AB + \overline{C} \): This portion suggests an OR operation between the result of ANDing variables \( A \) and \( B \), and the NOT operation on variable \( C \). - \( \overline{B} + C \): This portion indicates an OR operation between the NOT operation on variable \( B \) and variable \( C \). - The overall expression multiplies (AND operation) the results of the two OR operations mentioned above. **Logic Diagram with Gates:** While the logic diagram is not depicted in the image, based on the expression, it would typically involve: - An AND gate for the entire expression \( X \). - OR gates for each inner part of the expression (\(AB + \overline{C}\) and \(\overline{B} + C\)). - NOT gates for the negations \(\overline{C}\) and \(\overline{B}\). **Purpose in Education:** This structure is used to teach students about constructing logic gates diagrams from Boolean algebra expressions, highlighting the use of AND, OR, and NOT operations in digital circuits design.
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The given logic function,

X=AB+C¯B¯+C

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