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 15E

a.

Program Plan Intro

Distributive law:

Consider three variables x, y, and z. The multiplication of variable (x) with the sum of two variables (y and z) is same as the sum of the products (xy and xz).

The representation of distributive law is as follows:

x + (yz) = (x + y) (x + z)x (y + z) = xy + xz

Identity law:

The sum of the variable (x) and the value 0 is “x” and the product of the variable (x) and the value 1 is “x”.

The representation of identity law is as follows:

0 + x = x x = x

Inverse law:

The sum of the variable (x) and the complement of the variable (x’) is 1 and the product of the variable (x) and the complement of the variable (x’) is 0.

The representation of inverse law is as follows:

x + x' = 1 x = 0

Idempotent law:

The sum of the variable (x) and the same variable (x) is “x” and the product of the variable (x) and the same variable (x) is “x”.

The representation of idempotent law is as follows:

x + x = x x = x

a.

Expert Solution
Check Mark

Explanation of Solution

Simplification:

F(x, y, z) = x(yz + y'z)+ xy + x'y + xz= xyz + xy'z + xy + x'y + xz            (by Distributive law)= x(y + y') + xy + x'y + xz                 (by Distributive law)= x(1) + xy + x'y + xz                         (by Inverse law)

= xz + xz + xy + x'y                               (by Identity law)= xz + xy + x'y                                        (by Idempotent law)= xz + y (x + x')                                         (by Distributive law)= xz + y (1)                                                (by Inverse law)= xz + y                                                      (by Identity law)

Therefore, the simplified expression is “xz+y”.

b.

Program Plan Intro

Distributive law:

Consider three variables x, y, and z. The multiplication of variable (x) with the sum of two variables (y and z) is same as the sum of the products (xy and xz).

The representation of distributive law is as follows:

x + (yz) = (x + y) (x + z)x (y + z) = xy + xz

Identity law:

The sum of the variable (x) and the value 0 is “x” and the product of the variable (x) and the value 1 is “x”.

The representation of identity law is as follows:

0 + x = x x = x

Inverse law:

The sum of the variable (x) and the complement of the variable (x’) is 1 and the product of the variable (x) and the complement of the variable (x’) is 0.

The representation of inverse law is as follows:

x + x' = 1 x = 0

De Morgan’s Law:

  • The complement of the intersection of two sets is the union of their complements.
  • The complement of the union of two sets is the intersection of their complements.

The representation of the De Morgan’s law as follows:

(xy)' = x' + y'(x + y)' = x'  y'

Double compliment law:

The representation of double compliment law is

x'' = x

b.

Expert Solution
Check Mark

Explanation of Solution

Simplification:

F(x, y, z) = xyz'' + (y + z)' + x'yz= xyz + (y + z)' + x'yz                (by Double Complement law)= xyz + (y'z') + x'yz                  (by DeMorgan's law)= yz(x + x') + y'z'                             (by Distributive law)

= yz(1) + y'z'                                    (by Inverse law)= yz + y'z'                                         (by Identity law)

Therefore, the simplified expression is “yz+y'z'”.

c.

Program Plan Intro

Distributive law:

Consider three variables x, y, and z. The multiplication of variable (x) with the sum of two variables (y and z) is same as the sum of the products (xy and xz).

The representation of distributive law is as follows:

x + (yz) = (x + y) (x + z)x (y + z) = xy + xz

Idempotent law:

The sum of the variable (x) and the same variable (x) is “x” and the product of the variable (x) and the same variable (x) is “x”.

The representation of idempotent law is as follows:

x + x = x x = x

Null law:

The sum of the variable (x) and the value 1 is “1” and the product of the variable (x) and the value 0 is “0”.

The representation of null law is as follows:

1 + x = 1 x = 0

Identity law:

The sum of the variable (x) and the value 0 is “x” and the product of the variable (x) and the value 1 is “x”.

The representation of identity law is as follows:

0 + x = x x = x

c.

Expert Solution
Check Mark

Explanation of Solution

Simplification:

F(x, y, z) = z(xy' + z)(x + y')= z((xy' + z)x +(xy' + z)y')                (by Distributive law)= z((xxy' + zx)+(xy'y' + zy'))         (by Distributive law)= z(xy' + zx + xy' + zy')                       (by Idempotent law)

= z(xy' + zx + zy')                                  (by Idempotent law)=zxy' + zzx + zzy'                             (by Distributive law)=zxy' + zx + zy'                                     (by Idempotent law)=zy' (x + 1)+ zx                                       (by Distributive law)

=zy' (1)+ zx                                              (by Null law)=zy' + zx                                                   (by Identity law)=z(y' + x)                                                   (by Distributive law)

Therefore, the simplified expression is “z(y'+x)”.

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!
Students have asked these similar questions
Need this expression solved for mu. This can be done using a symbolic toolbox, however it needs to end up being mu = function (theta, m, L, g). If using MATLAB or something similar, run the code to make sure it works.
A business case scenario and asked to formulate an appropriate software design solution. Theyshould complete the case and upload the solution.  will be required to read the case,identify and document the key issues, problems, and opportunities presented, and then design,and develop an appropriate integrated design solution to the problem.  mustdemonstrate good spreadsheet, database, analytical, and word-processing skills whendeveloping solutions. Additionally,  must be creative and demonstrate synthesising andapplying Database Management and Data Analytics Principles learned in the course. They willalso need to research some aspects of the assessment.   CASE BACKGROUNDMGMT SS STATS, an umbrella body that facilitates and serves various Social SecurityOrganizations/Departments within the Caribbean territories, stoodpoised to meet the needs of its stakeholders by launching an onlinedatabase at www.SSDCI.gov. The database will provide membersand the public access to the complete set of…
A business case scenario and asked to formulate an appropriate software design solution. Theyshould complete the case and upload the solution.  will be required to read the case,identify and document the key issues, problems, and opportunities presented, and then design,and develop an appropriate integrated design solution to the problem.  mustdemonstrate good spreadsheet, database, analytical, and word-processing skills whendeveloping solutions. Additionally,  must be creative and demonstrate synthesising andapplying Database Management and Data Analytics Principles learned in the course. They willalso need to research some aspects of the assessment.   CASE BACKGROUNDMGMT SS STATS, an umbrella body that facilitates and serves various Social SecurityOrganizations/Departments within the Caribbean territories, stoodpoised to meet the needs of its stakeholders by launching an onlinedatabase at www.SSDCI.gov. The database will provide membersand the public access to the complete set of…

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.
Similar questions
SEE MORE QUESTIONS
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