# Data Representation / Numbering Conversion / File Permissions

### Main Objectives of this Practice Tutorial

• Understand how digital computers store data (i.e. data representation)
• Define decimal, binary, octal and hexadecimal numbers
• Manually perform numbering conversions between the decimal, binary, octal and hexadecimal numbering systems
(without the use of a computer or calculator)
• Identify which numbering system conversion method to use when required to perform a numbering conversion
• Explain the purpose of file permissions
• Explain how permissions work differently for directories as opposed to regular files.
• Change file permissions with the chmod command (both symbolic and absolute methods)
• Use the umask command to automatically assign permissions for directory and regular files to be created.

### Tutorial Reference Material

 Course Notes Numbering Conversion / File Permissions Reference YouTube Videos Slides:PDF | PPTX Data Representation Definitions File Permission Concepts Introduction to File Permissions File Permission Commands Instructional Videos:

# KEY CONCEPTS

### Why Study Data Representation?

 A series of binary numbers form a byte to represent numbers.(Image licensed under cc) Bytes can be used to also represent characters. It is job of a program to know if bytes are used to represent numbers or characters. Learning to convert numbering systems(like Hexadecimal to Binary) can be used to know how a character is represented in binary. (Image licensed under cc)

Data ... is any sequence of one or more symbols given meaning by specific act(s) of interpretation. Digital data is data that is represented using the binary number system of ones (1) and zeros (0)...
Reference: https://en.wikipedia.org/wiki/Data_(computing)

Binary numbers are combined in a sequence to form a byte. Bytes are used to represent numbers or characters. How does the computer know which bytes represent a number or a letter? That is the job of programs that are created (including operating systems and application software) to perform that task.

Examples of Understanding Data Representation:

• Network Specialists: Building Large Networks via Sub-netting
• C Programming: Sending information over networks, files
• Web Development: Setting color codes for webpage background or text
• Allowing or Limiting Unix / Linux File Access: Setting permissions for files and directories

### Decimal / Binary / Octal / Hexadecimal Numbering Systems

The decimal numbering system .
(Image licensed under cc - modified by author).

Decimal Numbers

The decimal numbering system consists of digits consisting of numbers 0 to 9. The numbering system is based on sums of the power of 10 which provides a framework for mathematic calculations.

The fact that humans started counting on their fingers and thumbs most likely lead to the development of this numbering system.

Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 10. For example, units are 100, tens are 101, hundred are 102 which move in a right-to-left direction.

The binary numbering system.

Binary Numbers

The binary numbering system consists of digits containing the numbers 0 or 1. The numbering system is based on sums of the power of 2.

Digital computers have circuits which representing data in terms of voltage levels. Multiple circuits are used to represent data (in the form of binary numbers).

Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 2. For example, 20 , 21, 22, etc. which move in a right-to-left direction.

The octal and hexadecimal numbering systems consist of digits containing numbers 0 to 7 and 0 to F respectively. For hexadecimal numbers, values for 10 to 15 are represented by the characters A to F respectively. The octal and hexadecimal numbering system are based on sums of the power of 8 and 16 respectively.

Since 1 octal digit represents 3 binary digits and 1 hexadecimal digit represents 4 binary digits, octal and hexadecimal numbers are used as short-cuts to represent binary number.

### Numbering Conversion Methods

#### Method 1: Binary to Decimal

Performing a binary to decimal conversion.

When converting binary numbers to decimal numbers, perform the following steps:

1. Write down the binary number.
2. Starting from the right-side, draw L's below the binary number moving to the left
(refer to diagram on right).
3. Starting on the rightmost "L", multiply the value (placeholder) by 2 to the power of zero.
4. Continually repeat step #3 moving leftwards, increasing the power of 2 by 1
(refer to diagram on right).
5. Add up the results to obtain the decimal value equivalent.

NOTE: To convert octal and hexadecimal numbers to decimal, replace the number 2
(in red in the diagram to the right) with 8 (for octal) or 16 (for hexadecimal).

#### Method 2: Decimal to Binary

Performing a decimal to binary conversion.

When converting decimal numbers to binary numbers, perform the following steps:

1. Write down the decimal number to be converted.
2. On the right-side, write the number 1 and moving leftwards, keep doubling the numbers until that number is greater than the decimal number to be converted (refer to the diagram on the right).
3. Starting on the right-side of those doubled numbers, compare that number with the decimal number. If that number if less than or equal to the decimal number, then write a 1 below and subtract that number from the decimal number to get a remainder. If the number is greater than decimal number (or remainder), then write a 0 below.

4. Repeat step #3 (moving leftwards and comparing the number with the decimal's remainder)

NOTE: If you are converting to 8-bit, 32-bit, etc., add leading zeros if necessary.

#### Method 3: Octal to Binary / Binary to Octal

 Performing an binary to octal numbering conversion. Performing an octal to binary numbering conversion.

Binary to Octal

1. One octal number represents 3 binary numbers, so starting from right-side, group binary digits into groups of 3
2. Write (4)(2)(1) under each group of 3 binary numbers.
3. Multiply the value or "placeholder" (i.e. 0's and 1's) by the corresponding (4)(2)(1) for each group to obtain the octal number (refer to diagram of binary to octal conversion).

Octal to Binary

1. One octal number represents 3 binary numbers, so space-out
the octal numbers to make space for a binary number.
2. Write (4)(2)(1) under each octal number.
3. Write 0's or 1's for each group of binary numbers to add up to the
corresponding octal number (refer to diagram of octal to binary conversion).

 Performing a binary to hexadecimal conversion. Performing a hexadecimal to binary conversion.

1. One hexadecimal number represents 4 binary numbers, so starting from right-side, group binary digits into groups of 4 (add leading zeros if necessary).
2. Write (8)(4)(2)(1) under each group of 4 binary numbers.
3. Multiply the values or "placeholders" (i.e. 0's and 1's) by the corresponding (8)(4)(2)(1) for each group to obtain the octal number.
4. Convert values from 10 to 15 to A to F
(refer to diagram of binary to hexadecimal conversion)

1. One hexadecimal number represents 4 binary numbers,
so space-out the hexadecimal numbers to make space for a binary number.
2. Convert letters A to F to 10 to 15 (refer to diagram of binary to hexadecimal conversion)
3. Write (8)(4)(2)(1) under each hexadecimal number.
4. Write 0's or 1's for each group of binary numbers to add up to the corresponding

For conversions between octal and hexadecimal numbers, use binary as a bridge.

To convert using the method, simply use binary as a "bridge".

Example:

To convert octal to hexadecimal, convert octal to binary, then convert binary to hexadecimal.

To convert hexadecimal to octal, convert hexadecimal to binary, then convert binary to octal.

### File Permissions

Since the Unix / Linux operating systems allow for multiple user accounts it is essential
to have a system to share or limit access to directories and files contained in those different user accounts.

Detailed directory listing showing permissions for a directory
and a regular file.

When directories and regular files are created, they are assigned to an owner
(typically the username which is the creator). To allow or limit access to those files and directories, those files and directories are assigned to an initial group referred to as a "primary group".

Users that own those directories and regular files are referred to as users, users that belong within the same group are referred to as same group members, and those users are do NOT belong to a particular group are referred to as other group members.

NOTE: In this course, we cannot create groups or assign users to groups in the Matrix server.
Instead, you will learn how to those tasks when or if you take a Unix/Linux administration account.
On the other hand, you can change which user,
existing same group members or existing other group members can or cannot access a directory or regular file.

 Permissions of a directory that contain subdirectories and regular files. Permissions of a regular file contained within a directory.

File Permissions consist of two-layers:

First, the permissions of a directory that contains regular files, and second, permissions of the regular files themselves.

Permissions for Directory files have a different meaning than permissions for regular files:

• Referring to the left-most diagram above, read (r) permissions permit viewing directory contents, write (w) permissions allow subdirectories and regular files to be created in that directory, and execute (x) permissions permit access to that directory. These permissions relate to the 3 categories: user (owner), same group members, other group members.
• Referring to the rightmost diagram above, read (r) permissions permit viewing regular file contents, write (w) permissions allow file contents to be modified/edited, and execute (x) permissions permit the file to be run (e.g. running a program or shell script). Again, these permissions relate to the 3 categories: user (owner), same group members, other group members.

NOTE: The symbol dash "-" indicates that the permission is NOT granted.

The permissions of newly-created directories and regular files are automatically assigned via a user mask (we will discuss this shortly). In order to change permissions for directories and regular files, you would use the chmod command.

Changing File Permissions with 'chmod' command:

Symbolic Method:

The chmod can use symbols to add, remove, and set rwx permissions for user,
same group members, other group members or ALL categories:

CommandDescription
chmod ugo+x script.bashAdd execute permissions to the file script.bash so it can be run.
chmod u=rwx,go=x ~Set "pass-thru" permissions of your home directory for same group members and other group members to navigate to other subdirectories (that may have access / view permissions).
chmod go-w ~/sharedRemove write permissions for same group members and other group members for the directory ~/shared
chmod a=rx mySet read and execute permissions for the directory myfile.txt

Octal (Absolute) Method:

using octal numbers to represent setting file permissions.

You can use octal numbers to represent permissions.

Since 1 octal digit represents 3 binary digits, one octal digit can represent the rwx permission granted or NOT granted. The permissions rwz would be in the form of 3 binary digits (1 represents the permission granted and 0 represents the permission NOT granted.

NOTE: You can only use this method to set file permissions (as opposed to add or remove permissions).

CommandDescription
chmod 500 script.bashSet read and execute permissions for only the user for the file script.bash so it can be run.
chmod 711 ~Set "pass-thru" permissions of your home directory for same group members and other group members to navigate to other subdirectories (that may have access / view permissions).
chmod 750 ~/sharedSet full permissions for user, read and access permissions for some group members and no permissions for other group members for the directory ~/shared
chmod 555 myfile.txtSet read and execute permissions for the directory myfile.txt

NOTE: You can use the -R option to set permissions for directory, subdirectory and directory contents recursively.

Setting Permissions for Newly-Created Directories and Regular Files (umask):

The umask command is used to set the permissions of newly-created directories and regular files.

Issuing the umask command without arguments will display the current umask value. Refer to the diagrams on the right-side to set the umask value for directories and regular files. Setting the umask value (for example umask 022) only takes effect for the current shell session unless the umask command is contained in a start-up file
(e.g. .profile, .bash_profile, or .bashrc).

# INVESTIGATION 1: NUMBERING CONVERSIONS

For this investigation, we will NOT be logged into our Matrix account, but it is recommended to have sheets of paper ready to manually perform numbering conversions.

NOTE: It is essential that you learn how to manually perform numbering conversions since you will NOT be permitted to perform quizzes, midterm, or your final exam with a computer or a calculator. Learning to quickly perform manual numbering conversions will may IT professional more productive such as setting permissions, designing computer networks, or selecting complex colors when developing webpages.

Only use a calculator to check your numbering conversion AFTER you have performed the operation manually.

You will now get practice performing numbering conversions.

Perform the Following Steps:

1. Let's convert the following 8-bit binary number 10111110 to a decimal number.

NOTE: It is important to learn and memorize the correct techniques to perform the
proper numbering conversion method (i.e. view the method above (drawing the L's).

2. Write the manual conversion on a sheet of paper.

3. Use a calculator to check your work. In MS Windows, you can set the calculator to Programming mode
by making the selection to binary, enter the binary number 10111110 and view the decimal equivalent.

Did you get the correct answer? If not, retry the method and check to see what you did wrong.

4. Perform a manual conversion of the decimal number 55 to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.

5. Perform a manual conversion of the octal number 461 to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.

6. Perform a manual conversion of the 8-bit binary number 11110001 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.

7. Perform a manual conversion of the hexadecimal number ABC to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.

8. Perform a manual conversion of the binary number 10101111 to an octal number.
What method (displayed above) will you use? Use a calculator to check your work.

9. Perform a manual conversion of the same binary number 10101111 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.

10. Perform a manual conversion of the octal number 5636 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.

11. Perform a manual conversion of the hexadecimal number D68 to an octal number.
What method (displayed above) will you use? Use a calculator to check your work.

12. When you have performed all of the numbering conversions above, then you can proceed to the next INVESTIGATION.

# INVESTIGATION 2: FILE PERMISSIONS

In this section, you will get experience using the chmod and umask commands
to set permissions for directories and files.

Perform the Following Steps:

1. Login your matrix account and issue a command to confirm you are located in your home directory.

2. Issue a single Linux command to create the following directory structure displayed in the diagram to the right.

NOTE: You will now run a shell script to confirm that you properly created that directory structure in your Matrix account.

4. Issue the following Linux command to run a checking script:
bash /home/murray.saul/scripts/week4-check-1

5. If you encounter errors and re-run the checking script until you receive a congratulations message, then you can proceed.

6. Issue Linux commands to create empty files for each of those newly created directories as show in diagram to the right:

NOTE: You will now run another shell script to confirm that you properly created those empty files within those specified directories.

7. Issue the following Linux command to run a checking script:
bash /home/murray.saul/scripts/week4-check-2

8. If you encounter errors and re-run the checking script until you receive a congratulations message, then continue the remaining steps.

Let's get practice understanding permissions, changing permissions, and setting your Linux account to automatically set permissions for newly created directories and regular files.

9. Issue the following Linux commands:
ls -ld ~/documents ~/clients ~/vendors
ls -lR ~/documents ~/clients ~/vendors

NOTE: You should see permissions already set for those newly created directories and regular files. What do these permissions mean for same group member and other group member access to those directory and regular files?

10. Let's limit access to the clients and vendors directories to only yourself and same group members. Issue the following Linux command:
chmod 750 ~/clients ~/vendors

11. Issue the ls command to confirm that the permissions for those directories have been changed.

NOTE: The -R option for the chmod command can change the file permissions recursively within a directory structure.

12. Issue the following Linux command: chmod 750 -R ~/documents

13. Again, use the ls command to confirm the permissions for the ~/documents, ~/document/memos , ~/documents/reports, and ~/documents/contracts directories.

14. Issue the following Linux command: ls -lR ~/documents
What do you noticed happened to the permissions for the regular files contained in those directories. Did those regular file permissions change?

We want to now change those regular file permissions to the following settings: r w - r - - - - -

15. Issue the following Linux commands:
chmod 740 ~/documents/memos/memo*.txt
chmod 740 ~/documents/reports/report*.txt
chmod 740 ~/dcouments/contracts/contract*.txt

16. Issue the ls -lR command for the ~/documents directory to confirm that those regular file permission have changed.

Let's get some practice setting permissions to allow users to make editing changes to regular files.

17. Issue the following Linux command: chmod ugo-w ~/documents/memos/memo*.txt

18. Use the ls command to verify that those regular file's permissions have changed.

19. Using the nano or vi text editor, open the regular file ~/documents/memos/memo1.txt, type in some text and try to save your editing changes.
What happened?

20. To abort your editing session in vi, type :q! and to abort your editing changes in nano, just type n when prompted to save editing changes

21. Issue the following Linux command to add write permissions for all files in the memos directory for yourself (i.e. user): chmod u+w ~/documents/memos/*

22. Repeat the previous step #19. What happened?

23. Issue the following Linux command to view permissions for your home directory: ls -ld ~

What does execute permissions mean for same group members and other group members in terms of your home directory?

24. Issue the following Linux command to create a new subdirectory: mkdir ~/shared

25. Issue the following Linux command: ls -l ~/shared

What are the permissions for this newly-created directory? Can other users access the directory pathname ~youruserid/shared ?

26. Issue the following Linux command (without an argument): umask

NOTE: You should see a four-digit octal number. Drop the leading zero on the left to obtain the default umask value.

27. Perform a mathematical calculation by taking the octal number 777 and subtracting the default umask value you determined in the previous step.
What is the result?

28. Convert that octal number result to a binary number. What does that represent as newly created directory permissions?
Does that correspond to the permissions for the newly created ~/shared directory?

29. Repeat steps #27 and #28 to see how a umask setting of 077 would affect permissions of newly-created directories.

30. Issue the following Linux command: umask 077
31. Issue the following Linux command (without arguments): umask

NOTE: You should notice the value 0077. By dropping the leading zero to the left, that would provide the default umask value of 077.

32. Issue the following Linux command: mkdir ~/shared2

33. Issue the following Linux command: ls -ld ~/shared2

Do the permissions for this newly created directory match the predicted permissions that you calculated in step #29?

34. Issue the following Linux command to create an empty regular file called myfile.txt in the ~/shared2 directory: touch ~/shared2/myfile.txt

35. Use the ls -l command to view the permissions for this newly created regular file.

What do you notice about those permissions?

36. Logout of your Matrix account, and then log-back into your Matrix account.

37. Issue the following Linux command (without arguments): umask

What happened? Referring to your notes, what do you need to do to make that umask value persistent?

38. After you complete the Review Questions sections to get additional practice, then work on your online assignment 2
and complete the sections 1 and 2 labelled: Practice Using The vi Text Editor and Permissions respectively.

# LINUX PRACTICE QUESTIONS

The purpose of this section is to obtain extra practice to help with your assignment #1, quizzes, your midterm, and your final ezam.

Here is a link to the MS Word Document of ALL of the questions displayed below but with extra room to answer on the document to simulate a quiz:

Your instructor may take-up these questions during class. It is up to the student to attend classes in order to obtain the answers to the following questions. Your instructor will NOT provide these answers in any other form (eg. e-mail, etc).

Review Questions:

1. List the number of digits for the following numbering systems:
• Decimal
• Binary
• Octal

2. Write a simple chart to show which values are represented for letter A - F for a hexadecimal number.
3. How many binary digits does 1 octal digit represent?
4. How many binary digits does 1 hexadecimal digit represent?
5. Use manual numbering conversion to complete the table displayed to the right.

1. Write the chmod command (using the symbolic method) to set “pass-through” permissions
(eg. r w x - - x - - x) for your home directory using an absolute pathname.
Write a Linux command to verify that permissions where set.

2. Perform a binary to octal numbering conversion for the permissions: r w x - - x - - x
Write single Linux command to set “pass-through” permissions for your home directory,
using the absolute method (i.e. octal numbers).

3. Write a single Linux command to add read permissions for same group members for the ~/tests directory.

4. Write a single Linux command to remove write permissions for same group members
and other group members for the ~/projects directory. Use the symbolic method.

5. Write a single Linux command to set the permissions for the ~/assignments directory
to the following using the absolute method (i.e. octal numbers): r w x r - x - - x
Show your work to perform a binary to octal conversion.
Write the command below using octal numbers and using a relative-to-home pathname.

6. Assume that you just issued the command:
chmod u=rwx,go=x ~/linux/content
What would be the new permissions for the “content” directory?

7. Assume that you just issued the commands: