2. Assume you have the following truth tables for functions F₁(x, y, z) and F₂(x, y, z): XO X 0 0 0 0 1 1 1 1 HOOLD NOH 0 0 1 1 0 1 0 0 0 1 1 0 1 1 Z 1 0 F₁ F₂ 1 1 0 0 0 1 0 0 нононп 0 1 0 a) Express F₁ and F₂ in sum-of-products form b) Simplify each function

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
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**Question 2: Analysis of Truth Tables for Functions \( F_1(x, y, z) \) and \( F_2(x, y, z) \)**

Given are the truth tables for two functions \( F_1 \) and \( F_2 \). Here's the provided information:

| x | y | z | \( F_1 \) | \( F_2 \) |
|---|---|---|------|------|
| 0 | 0 | 0 |   1  |   1  |
| 0 | 0 | 1 |   1  |   0  |
| 0 | 1 | 0 |   0  |   1  |
| 0 | 1 | 1 |   0  |   0  |
| 1 | 0 | 0 |   0  |   1  |
| 1 | 0 | 1 |   1  |   0  |
| 1 | 1 | 0 |   0  |   1  |
| 1 | 1 | 1 |   0  |   0  |

### Tasks:

**a) Express \( F_1 \) and \( F_2 \) in sum-of-products form**

- **Sum-of-Products for \( F_1 \):**  
  \( F_1 = \overline{x} \ \overline{y} \ \overline{z} + \overline{x} \ \overline{y} \ z + x \ \overline{y} \ z \)

- **Sum-of-Products for \( F_2 \):**  
  \( F_2 = \overline{x} \ \overline{y} \ \overline{z} + \overline{x} \ y \ \overline{z} + x \ \overline{y} \ \overline{z} + x \ y \ \overline{z} \)

**b) Simplify each function**

- **Simplified form of \( F_1 \):**  
  \( F_1 = \overline{x} \ \overline{y} + x \ \overline{y} \ z \)

- **Simplified form of \( F_2 \):**
Transcribed Image Text:**Question 2: Analysis of Truth Tables for Functions \( F_1(x, y, z) \) and \( F_2(x, y, z) \)** Given are the truth tables for two functions \( F_1 \) and \( F_2 \). Here's the provided information: | x | y | z | \( F_1 \) | \( F_2 \) | |---|---|---|------|------| | 0 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 0 | 1 | | 1 | 1 | 1 | 0 | 0 | ### Tasks: **a) Express \( F_1 \) and \( F_2 \) in sum-of-products form** - **Sum-of-Products for \( F_1 \):** \( F_1 = \overline{x} \ \overline{y} \ \overline{z} + \overline{x} \ \overline{y} \ z + x \ \overline{y} \ z \) - **Sum-of-Products for \( F_2 \):** \( F_2 = \overline{x} \ \overline{y} \ \overline{z} + \overline{x} \ y \ \overline{z} + x \ \overline{y} \ \overline{z} + x \ y \ \overline{z} \) **b) Simplify each function** - **Simplified form of \( F_1 \):** \( F_1 = \overline{x} \ \overline{y} + x \ \overline{y} \ z \) - **Simplified form of \( F_2 \):**
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