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
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
Section: Chapter Questions
Problem 1PE
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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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