**Problem Statement:****3) Simplify the following Boolean functions, using K-maps. F(w, x, y, z) = Σ(1, 3, 4, 5, 6, 7, 9, 11, 13, 15) (4 pts)**---**Explanation:**In this problem, you are required to simplify the given Boolean function using Karnaugh maps (K-maps). The function is provided in the form of a minterm list:\[F(w, x, y, z) = \Sigma(1, 3, 4, 5, 6, 7, 9, 11, 13, 15)\]A Karnaugh map is a diagram used in Boolean algebra and digital logic design for the simplification of algebraic expressions. The K-map for a four-variable function (w, x, y, z) will be a 4x4 grid where each cell represents a minterm corresponding to the binary values of the variables.**Steps to Solve:**1. **Draw a 4-variable K-map:** - Label the K-map rows and columns to represent the binary values of the variables. - Fill in the cells corresponding to the given minterms with a 1. All other cells will have a 0.2. **Group the 1s into rectangles:** - Each group (rectangle) should contain 1, 2, 4, or 8 cells. - Each group must be as large as possible. - Groups can wrap around the edges of the K-map.3. **Write down the simplified expression:** - For each group, determine the common variables and their corresponding values. - Combine the terms to form the simplified Boolean expression.**Note:** Since the image does not contain an actual K-map diagram or visual graphs, the explanation here is to guide students on how to approach simplifying the given Boolean function using a Karnaugh map. Drawing the K-map and performing the simplification step-by-step will lead to the required simplification.

A Karnaugh map, often referred to as a K-map, is a graphical method used for simplifying Boolean…

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3) Simplify the following Boolean functions, using K-maps. F(w, x, y, z) = (1, 3, 4, 5, 6, 7, 9, 11, 13, 15) (4 pts)

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

Chapter1: Introduction

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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

**Problem Statement:**

**3) Simplify the following Boolean functions, using K-maps. F(w, x, y, z) = Σ(1, 3, 4, 5, 6, 7, 9, 11, 13, 15) (4 pts)**

---

**Explanation:**

In this problem, you are required to simplify the given Boolean function using Karnaugh maps (K-maps). The function is provided in the form of a minterm list:

\[F(w, x, y, z) = \Sigma(1, 3, 4, 5, 6, 7, 9, 11, 13, 15)\]

A Karnaugh map is a diagram used in Boolean algebra and digital logic design for the simplification of algebraic expressions. The K-map for a four-variable function (w, x, y, z) will be a 4x4 grid where each cell represents a minterm corresponding to the binary values of the variables.

**Steps to Solve:**

1. **Draw a 4-variable K-map:**
- Label the K-map rows and columns to represent the binary values of the variables.
- Fill in the cells corresponding to the given minterms with a 1. All other cells will have a 0.

2. **Group the 1s into rectangles:**
- Each group (rectangle) should contain 1, 2, 4, or 8 cells.
- Each group must be as large as possible.
- Groups can wrap around the edges of the K-map.

3. **Write down the simplified expression:**
- For each group, determine the common variables and their corresponding values.
- Combine the terms to form the simplified Boolean expression.

**Note:** Since the image does not contain an actual K-map diagram or visual graphs, the explanation here is to guide students on how to approach simplifying the given Boolean function using a Karnaugh map. Drawing the K-map and performing the simplification step-by-step will lead to the required simplification.

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4. Karnaugh Maps Simplify parts a through d using Karnaugh maps a) F(x.y.)-Σ(0,2,4,5) b) F(x,y,z)=x'y'+yz+x'yz' c) F(w,x,y,z)=E(2,3,12,13,14,15) d) x'z+w'xy'+w(x'y+xy') e) Find minterms of xy+yz+xy'z by plotting it in a Karnaugh map. f) Find all the prime implicants of F (w, x, y, z)=E(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) Determine which are essential. g) Simplify F (A, B, C, D)=E(1, 3, 4, 5, 10, 11, 12, 13, 14, 15) using essential prime implicants.