Please use four variables K-map and show your work on a paper ### Simplification of a Boolean Function Using a Four-Variable K-map#### Problem Statement:Simplify the following Boolean function using a four-variable Karnaugh map (K-map).\[ F(A, B, C, D) = \Sigma(2, 3, 6, 7, 12, 13, 14) \]### Explanation:In this problem, we are given a Boolean function \( F \) defined by the sum of minterms. The minterm indices provided are 2, 3, 6, 7, 12, 13, and 14. These indices represent the binary combinations of the variables \( A \), \( B \), \( C \), and \( D \).### Steps for Simplification Using K-map:1. **Construct the K-map**: A four-variable K-map has 16 cells, corresponding to each combination of \( A, B, C, \) and \( D \).2. **Populate the K-map**: - Mark ‘1’ in the cells corresponding to the minterms given in the function. - The K-map for this problem will look like this: | AB\CD | 00 | 01 | 11 | 10 | |------|----|----|----|----| | 00 | 0 | 0 | 0 | 0 | | 01 | 0 | 1 | 1 | 0 | | 11 | 0 | 1 | 1 | 0 | | 10 | 0 | 1 | 1 | 1 |3. **Simplify**: - Group adjacent 1s in the K-map into rectangles containing 1, 2, 4, or 8 cells. - The goal is to cover all 1s using the fewest number of groups. 4. **Write the simplified Boolean expression**: - Each group you form in the K-map translates to a term in the simplified Boolean expression.### Final Simplified Expression:After mapping and grouping the minterms from the K-map, you derive the simplified Boolean expression.\[ F(A, B, C, D) = AC' + AD' \]This simplification process minimizes the original Boolean function to its simplest form for

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Answered: 2 Simplify the following Boolean…

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2 Simplify the following Boolean function, using four variables K-map. F(A, B, C, D) = Σ(2, 3, 6, 7, 12, 13, 14)

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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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.

Question

Please use four variables K-map and show your work on a paper

### Simplification of a Boolean Function Using a Four-Variable K-map

#### Problem Statement:
Simplify the following Boolean function using a four-variable Karnaugh map (K-map).

\[ F(A, B, C, D) = \Sigma(2, 3, 6, 7, 12, 13, 14) \]

### Explanation:
In this problem, we are given a Boolean function \( F \) defined by the sum of minterms. The minterm indices provided are 2, 3, 6, 7, 12, 13, and 14. These indices represent the binary combinations of the variables \( A \), \( B \), \( C \), and \( D \).

### Steps for Simplification Using K-map:
1. **Construct the K-map**:
A four-variable K-map has 16 cells, corresponding to each combination of \( A, B, C, \) and \( D \).

2. **Populate the K-map**:
- Mark ‘1’ in the cells corresponding to the minterms given in the function.
- The K-map for this problem will look like this:

| AB\CD | 00 | 01 | 11 | 10 |
|------|----|----|----|----|
| 00 | 0 | 0 | 0 | 0 |
| 01 | 0 | 1 | 1 | 0 |
| 11 | 0 | 1 | 1 | 0 |
| 10 | 0 | 1 | 1 | 1 |

3. **Simplify**:
- Group adjacent 1s in the K-map into rectangles containing 1, 2, 4, or 8 cells.
- The goal is to cover all 1s using the fewest number of groups.

4. **Write the simplified Boolean expression**:
- Each group you form in the K-map translates to a term in the simplified Boolean expression.

### Final Simplified Expression:
After mapping and grouping the minterms from the K-map, you derive the simplified Boolean expression.

\[ F(A, B, C, D) = AC' + AD' \]

This simplification process minimizes the original Boolean function to its simplest form for

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