Essentials of Computer Organization and Architecture
Essentials of Computer Organization and Architecture
5th Edition
ISBN: 9781284123036
Author: Linda Null
Publisher: Jones & Bartlett Learning
bartleby

Videos

Question
Book Icon
Chapter 3, Problem 33E
Program Plan Intro

a.

K-Map:

  • K-Map stands for Karnaugh Map which is used to reduce the logic functions more easily and quickly.
  • It will minimize the Boolean expressions without using Boolean algebra theorems.
  • By using K-Map, the Boolean expressions with two to four variables are easily reduced.

Expert Solution
Check Mark

Explanation of Solution

Simplification of Boolean expression using K-Map:

 Given:

 F(x, y, z)=w'x'y'z' + w'x'yz' + w'xy'z +   w'xyz  + w'xyz' +  wx'y'z' + wx'yz'

 The K-Map for the given expression is as follows:

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  1

 The following steps are used to obtain the simplified Boolean expressions.

 Step1:

 Then group another possible 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  2

     F = w'x'y'z' + w'x'yz' + wx'y'z' + wx'yz'= w'x'z'(y'+y) + wx'z'(y'+y)=w'x'z'(1) + wx'z'(1)=w'x'z' + wx'z'

        =(w' + w)x'z'=(1)x'z'=x'z'

 Step2:

  The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  3

     F = w'xy'z + w'xyz= w'xz(y'+y)=w'xz(1)=w'xz

 Step3:

  The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  4

     F = w'xyz + w'xyz'= w'xy(z'+z)=w'xy(1)=w'xy

 Step4:

 Group all the expressions

 F = x'z' + w'xz + w'xy

 Therefore, the simplified expression is “F = x'z' + w'xz + w'xy”.

Program Plan Intro

b.

K-Map:

  • K-Map stands for Karnaugh Map which is used to reduce the logic functions more easily and quickly.
  • It will minimize the Boolean expressions without using Boolean algebra theorems.
  • By using K-Map, the Boolean expressions with two to four variables are easily reduced.

Expert Solution
Check Mark

Explanation of Solution

Simplification of Boolean expression using K-Map:

 Given:

 F(x, y, z)=w'x'y'z' + w'x'y'z + wx'y'z + wx'yz' + wx'y'z'

 The K-Map for the given expression is as follows:

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  5

 The following steps are used to obtain the simplified Boolean expressions.

 Step1:

 The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  6

     F = w'x'y'z' + w'x'y'z + wx'y'z' + wx'y'z= w'x'y'(z' + z)+ wx'y'(z' + z)=w'x'y'(1)+ wx'y'(1)=w'x'y'+ wx'y'

        =(w' + w)x'y'=(1)x'y'=x'y'

 Step2:

 The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  7

     F = wx'y'z' + wx'yz'= wx'z'(y' + y)=wx'z'(1)=wx'z'

 Step3:

 Group all the expressions

 F = x'y' + wx'z'

 Therefore, the simplified expression is “F = x'y' + wx'z'”.

Program Plan Intro

c.

K-Map:

  • K-Map stands for Karnaugh Map which is used to reduce the logic functions more easily and quickly.
  • It will minimize the Boolean expressions without using Boolean algebra theorems.
  • By using K-Map, the Boolean expressions with two to four variables are easily reduced.

Expert Solution
Check Mark

Explanation of Solution

Simplification of Boolean expression using K-Map:

 Given:

 F(x, y, z)=y'z + wy' + w'xy + w'x'yz' + wx'yz'(x' + x)y'z(w' + w)+  w(x' + x)y'(z' + z) +  (z' + z)w'xy + w'x'yz' + wx'yz'

                 =  wxy'z+ w'xy'z+ wx'y'z+ w'x'y'z   wxy'z + wxy'z' + wx'y'z + wx'y'z' +    w'xyz + w'xyz'+ w'x'yz'+ wx'yz'

 The K-Map for the given expression is as follows:

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  8

 The following steps are used to obtain the simplified Boolean expressions.

 Step1:

 Then group another possible 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  9

  F = wxy'z'+ wxy'z+ wx'y'z'+ wx'y'z= wxy'(z+z') + wx'y'(z+z')=wxy'(1) + wx'y'(1)=wy'(x + x')

           =wy'

 Step2:

 The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  10

     F = w'x'y'z+ w'xy'z+ wxy'z+ wx'y'z= w'y'z(x+x') + wy'z(x+x')=w'y'z(1) + wy'z(1)=y'z(w + w')

                = y'z

 Step3:

 The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  11

     F = wx'y'z'+ wx'yz'= wx'z'(y+y')=wx'z'(1)=wx'z'

 Step4:

 The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  12

     F = w'x'yz'+ w'xyz'= w'yz'(x+x')=w'yz'(1)=w'yz'

 Step5:

 The group the 1’s in the table. Then write the Boolean expression according to the mapping. Write 0 term’s as complemented variable like x’ and 1 term’s as it is like x.

Essentials of Computer Organization and Architecture, Chapter 3, Problem 33E , additional homework tip  13

     F = w'xyz+ w'xyz'= w'xy(z+z')=w'xy(1)=w'xy

 Step6:

 Group all the expressions

 F = y'z + w'yz' + w'xy + wy' + wx'z' 

 Therefore, the simplified expression is “F = y'z + w'yz' + w'xy + wy' + wx'z' ”.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 3 Solutions

Essentials of Computer Organization and Architecture

Ch. 3 - Prob. 11RETCCh. 3 - Prob. 12RETCCh. 3 - Prob. 13RETCCh. 3 - Prob. 14RETCCh. 3 - Prob. 15RETCCh. 3 - Prob. 16RETCCh. 3 - Prob. 17RETCCh. 3 - Prob. 18RETCCh. 3 - Prob. 19RETCCh. 3 - Prob. 20RETCCh. 3 - Prob. 21RETCCh. 3 - Prob. 22RETCCh. 3 - Prob. 23RETCCh. 3 - Prob. 24RETCCh. 3 - Prob. 25RETCCh. 3 - Prob. 26RETCCh. 3 - Prob. 1ECh. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 7ECh. 3 - Prob. 8ECh. 3 - Prob. 9ECh. 3 - Prob. 10ECh. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 35ECh. 3 - Prob. 36ECh. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40ECh. 3 - Prob. 41ECh. 3 - Prob. 42ECh. 3 - Prob. 43ECh. 3 - Prob. 44ECh. 3 - Prob. 45ECh. 3 - Prob. 46ECh. 3 - Prob. 47ECh. 3 - Prob. 48ECh. 3 - Prob. 49ECh. 3 - Prob. 50ECh. 3 - Prob. 51ECh. 3 - Prob. 52ECh. 3 - Prob. 53ECh. 3 - Prob. 54ECh. 3 - Prob. 55ECh. 3 - Prob. 56ECh. 3 - Prob. 57ECh. 3 - Prob. 58ECh. 3 - Prob. 59ECh. 3 - Prob. 60ECh. 3 - Prob. 61ECh. 3 - Prob. 62ECh. 3 - Prob. 63ECh. 3 - Prob. 64ECh. 3 - Prob. 65ECh. 3 - Prob. 66ECh. 3 - Prob. 67ECh. 3 - Prob. 68ECh. 3 - Prob. 70ECh. 3 - Prob. 71ECh. 3 - Prob. 72ECh. 3 - Prob. 73ECh. 3 - Prob. 74ECh. 3 - Prob. 75ECh. 3 - Prob. 76ECh. 3 - Prob. 77ECh. 3 - Prob. 78ECh. 3 - Prob. 79ECh. 3 - Prob. 80E
Knowledge Booster
Background pattern image
Computer Science
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.
Recommended textbooks for you
Text book image
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Text book image
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Text book image
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
Text book image
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Text book image
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Boolean Algebra - Digital Logic and Logic Families - Industrial Electronics; Author: Ekeeda;https://www.youtube.com/watch?v=u7XnJos-_Hs;License: Standard YouTube License, CC-BY
Boolean Algebra 1 – The Laws of Boolean Algebra; Author: Computer Science;https://www.youtube.com/watch?v=EPJf4owqwdA;License: Standard Youtube License