Data Representation
Why Study Data Representation?
- Computers process and store information in binary format
- For many aspects of programming and networking, the details of data representation must be understood
- C Programming - sending information over networks, files
- Unix / Linux - setting permissions for files and directories
- Web Pages - setting color codes
Data Representation
- In terms of this course, we will learn how a simple decimal number (integer) is stored into the computer system as a binary number.
- We will also learn other numbering systems (octal and hexadecimal) that can be used as a “short-cut” to represent binary numbers.
- Before we learn numbering systems, we have to “goback in time” to see how we learned the decimal numbering system.
- The decimal numbering system (base 10) uses 10 symbols for each digit (0, 1, 2, … 9). Since most humans have 10 extensions on their hands (2 thumbs, 8 fingers), many suspect that is why humans work with decimal numbers.
Decimal Numbers
In grade school, we probably learned to break-down, as follows, the decimal 3572:
3 thousands 5 hundreds 7 tens 2 ones
Another way to look at this number is multiplying the digit by 10 (the numbering base) raised to increasing powers (starting at 0 from the “ones” and moving towards the higher digits)
3 thousands = 3 x 10^3 = 3 x 1000 5 hundreds = 5 x 10^2 = 5 x 100 7 tens = 7 x 10^1 = 7 x 10 2 ones = 2 x 10^0 = 2 x 1
This way of understanding decimal numbers is the basis for math operations such as addition, subtraction, multiplication, decimal numbers, etc!
Binary Numbers
We can use a similar method to convert a binary number to a decimal number. We do the same thing in the previous slide, but we multiply by base 2 instead of base 10. Take the binary number 1101:
1 x 2^3 = 1 x 8 = 8 + 1 x 2^2 = 1 x 4 = 4 + 0 x 2^1 = 0 x 2 = 0 + 1 x 2^0 = 1 x 1 = 1 --------------------- Sum of 8 + 4 + 0 + 1 = 13
Remember start from the right-hand-side and move to the left. Therefore, 1101 in binary is 13 in decimal. For programmers, the 8-bit binary number 00001101 represents the unsigned integer 13.
Octal Numbers
The octal numbering system (base 8) uses 8 symbols for each digit (0, 1, 2, … 7). We can use the same process to convert an octal number to a decimal number (but use base 8 instead). Convert the octal number 2741 to decimal:
2 x 8^3 = 2 x 512 = 1024 + 7 x 8^2 = 7 x 64 = 448 + 4 x 8^1 = 4 x 8 = 32 + 1 x 8^0 = 1 x 1 = 1 --------------------- Sum of 1024+448+32+1 = 1505
Remember, start from the right-hand-side and move to the left. Therefore, 2741 in octal is 1505 in decimal.
Hexadecimal Numbers
The hexadecimal numbering system (base 16) uses 16 symbols for each digit (0, 1, 2, … 9, A, B, C, D, E, F). Why use letters? Because we are only human and we need to use letters to represent higher digits 10 - 15 as a single digit! Let’s convert the hexadecimal number F2A to decimal:
F x 16^2 = 15 x 16^2 = 15 x 256 = 3840
2 x 16^1 = 2 x 16^1 = 2 x 16 = 32
A x 16^0 = 10 x 16^0 = 10 x 1 = 10
---------------------
3882
Therefore, F2A in Hexadecimal is 3882 in decimal. I can understand now how decimal numbers can be stored in the computers as binary numbers, but why are we learning Octal and Hexadecimal numbers? As computers and computer programming languages evolved, octal and hexadecimal numbers were considered “short-hand” a short-cut to represent binary numbers.
- Each octal digit represents 3 binary digits.
- Each hexadecimal digit represents 4 binary digits.
- Linux/Unix operating system commands, networking specialists, programming analysts as well as car-crash investigators use these types of shortcuts which help save space and time issuing a command. Cars provide hexadecimal codes to record info prior to impact. Hexadecimal numbers can refer to memory addresses which point to incorrect programming procedure.
-
chmod 700 secretfileUnix/Linux command to allow file read, write and execute access to the file’s owner only. - You will be converting between any number system whether it is from binary to decimal, binary to octal, decimal to binary, octal to hexadecimal, etc.
- The next series of slides provide interesting shortcut how to perform these numbering system conversions. The symbol ^ is used to represent “raised to the power of..”. For Example: 103 = 103
Converting Binary to Octal
- Convert the binary number
111110000to an octal number:
= 1 1 1 1 1 0 0 0 0 x 2^2 2^1 2^0 2^2 2^1 2^0 2^2 2^1 2^0 i.e. (4) (2) (1) (4) (2) (1) (4) (2) (1) 1x4+ 1x2+ 1x1 1X4+ 1x2+ 0x1 0X4+ 0x2+ 0x1 = 7 6 0
Therefore, the binary number 111110000 represents 760 as an octal number. This code can be used to represent directory and file permissions (you will learn how to set permissions soon)
Remember:
1 octal digit is equal to 3 binary digits. Group binary digits into groups of 3 starting from the right. Add leading zeros if left-most group has less then 3 digits. Convert each group of 3 digits to an octal digit.
Converting Octal to Binary
- Similar to previous calculation, but in reverse:
- Convert octal number
760to binary.
7 6 0 (4)(2)(1) (4)(2)(1) (4)(2)(1) 1 1 1 1 1 0 0 0 0 = 111110000
“Spread-out” octal number to make room for binary number result. Determine digits (0’s or 1’s) that are required when multiplied by appropriate power of 2 to add up to octal digit.
Converting Binary to Hex
- Convert the binary number
111110000to a hexadecimal number:
= 0 0 0 1 1 1 1 1 0 0 0 0 (8) (4) (2) (1) (8) (4) (2) (1) (8) (4) (2) (1) 1 15 0 1 F 0
Therefore, the binary number 111110000 represents 1F0 as a hexadecimal number.
1 hexadecimal digit is equal to 4 binary digits. Group binary digits into groups of 4 starting from the right. Add leading zeros if last group of digits is less than 4 digits. Convert each group of 4 digits to a hexadecimal digit.
Converting Hex to Binary
- Similar to previous calculation, but in reverse:
- Convert hexadecimal number
1F0to binary.
1 F 0 = 1 15 0 = (8)(4)(2)(1) (8)(4)(2)(1) (8)(4)(2)(1) = 0 0 0 1 1 1 1 1 0 0 0 0 = 000111110000 = 111110000
“Spread-out” hex number to make room for binary number result. Determine digits (0’s or 1’s) that are required when multiplied by appropriate power of 2 to add up to hexadecimal digit.
Converting decimal to binary
- Convert
78to a binary number - List the powers of 2 (until greater than or equal to 78) Start with the highest number equal or just less than 78. Put a binary digit “1” below that number and subtract that decimal equivalent from 78 (eg. 78 - 64 = 14). Repeat the same step for the remainder until result is zero. Any numbers NOT used become binary digit “0”
64 32 16 8 4 2 1 1 78-64=14 1 14- 8=6 1 6-4=2 1 2-2=0 0 0 0
File Permissions
As you may recall from our previous notes, that Unix/Linux recognizes everything as a file:
- Regular files to store data, programs, etc…
- Directory files to store regular files and subdirectories
- Special Device files which represent hardware such as hard disk drives, printers, etc… You may ask, “Since I can navigate throughout the Unix/Linux file system - what prevents someone from removing important files on purpose or by accident?” Answer: Ownership of the file, and file permissions.
- In previous classes, you only noted a few items from a detailed listing such as type of file, file size and date of creation/modification. Let’s look at the following detailed listing of a device (a harddisk partition) located in the /dev (devices) directory and explore more items: Let’s explore the results of this detailed listing in the next slide
[username] ls -l /dev/hda brw-r----- 1 root disk 3,0 2003-03-14 08:07 /dev/hda
This indicates the user who “owns” the file. In this case, the superuser or “root” probably created the file…
- File Type (i.e. “b” or “c” for device file, “-” for regular files, “d” for directory file)
- File Permissions (i.e. what permissions are granted by the owner regarding file access, file modification, and/or file execution).
- In this case, the owner (in this case root) can access (read) the file, the owner can modify (write) the file, but a dash instead of an “x” means that the owner cannot run (execute) the file like a program…
- OK, I can now see that the owner (root) is the only user that has permissions to make changes (write) to the file /dev/hda, so no other user can damage or edit and save changes to that file. But what if an owner of a file wanted other users to view or write to their file? Can the owner of the file allow access to some users, and not to others? Answer: That is what the other 2 sets of permissions are for.
[joe.professor] ls -l ~/work_together -rw-rw---- 1 joe.professor users 0 2006-02-02 10:47 ~/work_together # This indicates the user “joe.professor” owns the file “work_together”. # The owner “joe.professor” can read and write to that file. # By the way, you can change the ownership of files (using the chown command, assuming you own them). # Let’s look at the detailed listing for a regular file owned by someone else: [joe.professor] ls -l ~/work_together -rw-rw---- 1 joe.professor users 0 2006-02-02 10:47 ~/work_together # This indicates a group name (called “users”) that is assigned to that file “work_together”. # In this case the user “joe.professor” has given permission to other users that belong to the # “users” group to read and write to the file “work_together”. [joe.professor] ls -l ~/work_together -rw-rw---- 1 joe.professor users 0 2006-02-02 10:47 ~/work_together # What does this last set of permissions refer to? # Answer: all “other” users - users that DO NOT belong to the “users” group.!
Directory Permissions
- We use the same letters for permissions as for regular files and permissions are assigned for owner, group, and others
- However, since a directory is a special kind of file which holds lists of other files, permissions work differently than for regular files:
| r | allows listing contents of the directory |
| w | allows creating and deleting files inside |
| x | allows access to files inside |
- In order to have access to directory contents, at least the “x” permission is necessary.
This is called the “pass-through” permission. The pass-through permission is the key to grant access to only selected directories and/or files.
Consider this example- you are giving others access to the following:
/home/you/documents/uli101/jokes.txt- The following directories need pass-through permissions set by you for others: you, documents, uli101
- Even if the above directories have other files, possibly readable by others, they would have to know/guess their name before accessing them
- Just in case, you should not grant access permissions to others by default.
Only in specific case, such as this one (
jokes.txt), give read permissions to specific files
Changing Permissions via chmod command
chmod [permissions] file(s)
- Can be used to change permissions for directories and regular files.
- There are two ways to set [who][operation][permission]:
Symbolic Method (using characters)
Absolute Method (using Octal Numbers)
Symbolic Method
- Permissions are set for: user (u), group (g), others (o), or all (a)
- Permissions are set through: adding (+), removing (-) and/or setting (=)
- Permissions are set to: read (r), write (w) and execute (x)
Examples:
Add Permission chmod g+rw file1Remove Permission chmod g-w *txtSet Permission chmod o=rx /tmp/xyzCombined chmod u=rwx g+x o.=Octal Method
You can use the chmod command with 3 octal number to represent permissions for user, group and others In this method, each permission has a numerical value:
r = 4 w = 2 x = 1 The resulting/intended permission is the sum of the above, for example “rw” permission has a value of “6”, for example:
chmod 755 abc # abc permissions after: rwxr-xr-x chmod 531 abc # abc permissions afer: r-x-wx--x
umask
- Sets default file permissions for new files and directories in the current shell
- How does it work? umask permissions
For example: umask 467 Represents later: chmod 310
- Has the reverse effect to chmod - you set permissions which you do not want
- Each file permission is a subtraction result:
default 7 7 7 umask 4 6 7 = = = result 3 1 0 (for a directory)
- For ordinary files any execute permissions are no applied
- For example: umask 310 would result in permissions 466 (r--rw-rw-)