**Boolean Expression Reduction****Problem 12:** Reduce the following Boolean expressions. *Note:* The apostrophe (') denotes the logical NOT operation.For example, \( A'B \) means "Not A and B."**Expressions:**a. \( F = A'BC + AB'C + ABC' + ABC \)b. \( Y = A'C \cdot (A' + B) \cdot (B' + C) \)**Explanation:**- The expression \( A'BC + AB'C + ABC' + ABC \) involves multiple terms, each representing a minterm in Boolean algebra, where each letter represents a variable that can either be true (1) or false (0).- The expression \( A'C \cdot (A' + B) \cdot (B' + C) \) involves both AND (multiplication) and OR (addition) operations, with each operation needing appropriate handling according to Boolean laws. Use Boolean identities and laws, such as absorption, distribution, and De Morgan's theorems, to simplify these expressions.

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Answered: 12. Reduce the following Boolean…

12. Reduce the following Boolean expressions. Note: means Not Therefore, A'B _means Not A and B а. F3DA'BC + AВ'С + АВС" + АВс b. Y = A'C (A' + B) (B’ + C)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Question

**Boolean Expression Reduction**

**Problem 12:** Reduce the following Boolean expressions.

*Note:* The apostrophe (') denotes the logical NOT operation.

For example, \( A'B \) means "Not A and B."

**Expressions:**

a. \( F = A'BC + AB'C + ABC' + ABC \)

b. \( Y = A'C \cdot (A' + B) \cdot (B' + C) \)

<br>

**Explanation:**

- The expression \( A'BC + AB'C + ABC' + ABC \) involves multiple terms, each representing a minterm in Boolean algebra, where each letter represents a variable that can either be true (1) or false (0).
- The expression \( A'C \cdot (A' + B) \cdot (B' + C) \) involves both AND (multiplication) and OR (addition) operations, with each operation needing appropriate handling according to Boolean laws.

Use Boolean identities and laws, such as absorption, distribution, and De Morgan's theorems, to simplify these expressions.

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