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

As your requirement, I have provided hand-written solution image in next step--------------

Answered: 2 Simplify the following Boolean…

Engineering

Computer Science

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

See similar textbooks

Related questions

Q: What function does the computer graphics reflection vector serve? At least two examples should be…

A: Vector Reflection in Computer Graphics: To simulate reflecting objects like mirrors and bright…

Q: Hiow can it be done without using vectors

A: Answer:

Q: work out all answers

A: The objective of the question is to compute the angle between two vectors, the length of the…

Q: Write a program that asks the user to input a vector of integers of arbitrary length. Then, using a…

A: Take user input of vectorprint the original vectorcreate a modified vector as the same size of the…

Q: solve code in matlab

A: The objective of the question is to create a vector of elements from 0 to 15 in Matlab, calculate…

Q: Write a regular expression for the set of strings over the alphabet {a, b} that have at least one a…

A: Given that, Set of input alphabets= {a, b} The language must contains the set of strings which…

Q: 16. The set of strings over (a, b, c) with length three. 17. The set of strings over (a, b, c) with…

A: Set of strings over { a , b , c } with length 3 . The regular expression will be =( a + b + c ) (…

Q: determine positions along the circle octant in the first quadrant from x =0 ti x=y for a circle…

A: Midpoint circle algorithm is used to define the coordinates needed for rasterizing the circle.…

Q: A robot is initially located at position (0, 0) in a grid [−5, 5] × [−5, 5]. The robot can move…

A: Program code: //include the required header files #include <iostream> /* srand, rand */…

Q: Develop a program that creates a plot of the function f(x)= sin(1/(x+E)) for x in the unit interval,…

A: CODE # import modules import numpy as np import matplotlib.pyplot as plt # function def…

Q: can you show where indent is required

A: In this question we have to correct the indent the python code Let's code, hope this helps and I…

Concept explainers

Rod Cutting

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Summary

VIEW

Step 2: hand-written solution image

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Q1. Draw a wave that has a wavelength of 5m and an amplitude of 1m. Calculate the frequency?
CODE WITH COMMENTS AND OUTPUT SCREENSHOT is must for an Upvote
It cannot take decimal points as input. Please fix it.
Consider the circuit B 1. Derive the Boolean equations representing the outputs D = B = 2. Complete a truth table for the circuit Are both outputs minimized to the fewest number of literals/gates? Use the next page as workspace if needed. 3.
PYTHON JUPYTER NOTEBOOKS please show code clearly. create a program for lower triangular system L x = b. The algorithm is described in the image for i and j with offset 1. Recall that NumPy and Python have offset 0 for their sequence data types.
can you show a sample chart of this?
Question is in the photo attached Need a simple python code that does not involve the map() function
Below is the questions
Write a code that can be used to plot a 3D graph where x & y are between -5 to 5 and z is defined by the following equation. “z=4x4y - 3x3y2 + x”
Write an inline function to compute the perimeter of a rectangle of length l and width w (both l and w integers.)
How would I write the code to fix the function for for the drawBunny function to draw the Bunny as described, and supply the color of his ears and spot as a parameter