### Educational Content: Boolean SOP Expression for Truth Tables#### Problem Statement1. **Task**: Write a Boolean Sum of Products (SOP) expression for the given truth tables. Simplify the expressions as much as possible and draw the corresponding circuits for the simplified expressions.#### Truth Tables**a.**| A | B | C | Output ||---|---|---|--------|| 0 | 0 | 0 | 0 || 0 | 0 | 1 | 0 || 0 | 1 | 0 | 1 || 0 | 1 | 1 | 0 || 1 | 0 | 0 | 0 || 1 | 0 | 1 | 0 || 1 | 1 | 0 | 1 || 1 | 1 | 1 | 0 |**b.**| A | B | C | Output ||---|---|---|--------|| 0 | 0 | 0 | 0 || 0 | 0 | 1 | 0 || 0 | 1 | 0 | 1 || 0 | 1 | 1 | 1 || 1 | 0 | 0 | 0 || 1 | 0 | 1 | 0 || 1 | 1 | 0 | 0 || 1 | 1 | 1 | 1 |#### Explanation- **Truth Table a:** - The output is `1` when: - A = 0, B = 1, C = 0 - A = 1, B = 1, C = 0 - SOP Expression: \( \overline{A}BC + AB\overline{C} \) - Simplify this expression and draw the circuit.- **Truth Table b:** - The output is `1` when: - A = 0, B = 1, C = 0 - A = 0, B = 1, C = 1 - A = 1, B = 1, C = 1 - SOP Expression: \( \overline{A}B\overline

a. Output = B C' b. Output = A' B + C B

Answered: Write a Boolean SOP expression for this…

Write a Boolean SOP expression for this truth table, then simplify that expression as much as possible. Draw the circuits for simplified expressions.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

### Educational Content: Boolean SOP Expression for Truth Tables

#### Problem Statement
1. **Task**: Write a Boolean Sum of Products (SOP) expression for the given truth tables. Simplify the expressions as much as possible and draw the corresponding circuits for the simplified expressions.

#### Truth Tables

**a.**

| A | B | C | Output |
|---|---|---|--------|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |

**b.**

| A | B | C | Output |
|---|---|---|--------|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |

#### Explanation

- **Truth Table a:**
- The output is `1` when:
- A = 0, B = 1, C = 0
- A = 1, B = 1, C = 0
- SOP Expression: \( \overline{A}BC + AB\overline{C} \)
- Simplify this expression and draw the circuit.

- **Truth Table b:**
- The output is `1` when:
- A = 0, B = 1, C = 0
- A = 0, B = 1, C = 1
- A = 1, B = 1, C = 1
- SOP Expression: \( \overline{A}B\overline

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