**Title:** Boolean Expression Derivation**Objective:** Find the Boolean expression in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the given truth table.**Truth Table:**```| A | B | C | Y ||---|---|---|---|| 0 | 0 | 0 | 0 || 0 | 0 | 1 | 1 || 0 | 1 | 0 | 1 || 0 | 1 | 1 | 0 || 1 | 0 | 0 | 1 || 1 | 0 | 1 | 1 || 1 | 1 | 0 | 1 || 1 | 1 | 1 | 1 |```**Explanation:**- **Columns:** - **A, B, C:** Input variables. - **Y:** Output variable.- **Rows:** - The table lists all possible combinations of binary inputs (0s and 1s) and the corresponding output Y for each set of inputs.**Diagrams:**- No specific diagrams are present in this representation, as it is purely a tabular form.**Graph Explanation (Hypothetical):**- If there were a graph or diagram, it might visualize the truth table by mapping each input combination to the output using nodes for each state.**Next Steps (for Students):**1. **SOP Form:** - Identify rows where Y = 1 and write the product (AND) of literals for each row. - Sum (OR) these products together.2. **POS Form:** - Identify rows where Y = 0 and write the sum (OR) of literals for each row. - Product (AND) these sums together.Understanding how to interpret and convert truth tables into Boolean expressions is essential in digital logic design and computer engineering.

Sum of product (SOP):- this is define min terms 0 -----> complement 1 ------> normal…

Find the Boolean expression, in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the following truth table. A COO 0 0 0 0 1 1 1 1 BOO 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 HOT 0 1 Y 0 |TLOOTO 1 1 0 0 1 1

Find the Boolean expression, in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the following truth table. A COO 0 0 0 0 1 1 1 1 BOO 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 HOT 0 1 Y 0 |TLOOTO 1 1 0 0 1 1

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

**Title:** Boolean Expression Derivation

**Objective:** Find the Boolean expression in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the given truth table.

**Truth Table:**

```
| A | B | C | Y |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
```

**Explanation:**

- **Columns:**
- **A, B, C:** Input variables.
- **Y:** Output variable.

- **Rows:**
- The table lists all possible combinations of binary inputs (0s and 1s) and the corresponding output Y for each set of inputs.

**Diagrams:**

- No specific diagrams are present in this representation, as it is purely a tabular form.

**Graph Explanation (Hypothetical):**

- If there were a graph or diagram, it might visualize the truth table by mapping each input combination to the output using nodes for each state.

**Next Steps (for Students):**

1. **SOP Form:**
- Identify rows where Y = 1 and write the product (AND) of literals for each row.
- Sum (OR) these products together.

2. **POS Form:**
- Identify rows where Y = 0 and write the sum (OR) of literals for each row.
- Product (AND) these sums together.

Understanding how to interpret and convert truth tables into Boolean expressions is essential in digital logic design and computer engineering.

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