How Number System Is Used In It Applications Computer Science Essay


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In this documentation I have discussed of how the application of number system is used in IT applications in both hardware and applications, operating system and in programming language. I have discussed about the use of base 2 in the 8 bit bytes form use with the operation for subnet. The use of hexadecimal form addressing memory and classless inter Domain Routing.

There are number of different numbering system which is in use for the unique ability to represent different numbers. Binary, Octal, Denary and Hexadecimal are number systems that are used in different aspects Denary number is the most commonly used number system which is frequently used in daily life. Nevertheless each number system has associated benefits which are the reason that different number systems are used in different areas.

Each of the number system has a fix number of representation of numbers which are used to represent the numbers like, say for example Binary numbers are represented by either one or zero, Octal numbers are represented by numbers from 0, 1, 2, 3, 4, 5, 6, 7 whereas Denary and Hexadecimal numbers are represented by the number of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0, 1,2. 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, respectively.

Binary Numbers

Binary numbers are mostly used when there are only two options available so if one is false then the other is true. Examples of binary system can be their usage to represent bits in a computer which can have only 0 or 1 value a switch in a electric circuit which can be either on (1) or off (0). Binary system is widely used to represent situations in everyday normal life as well for example for electronic gates in electricity circuits, false or true statements can also be displaced in terms of binary digits where 0 represents false and 1 represents true states.

Denary Numbers

Denary numbers are frequently used in everyday life in accounting, calendar systems, financial systems or daily routine counting. The main benefits of Denary number system is that they are easier to use as compared to other number systems and have more number to present different situations though Hexadecimal number system has more representations but that representation can include characters in them as well which makes them more difficult to understand and use as compare to denary system. Denary number systems are so frequently used that a person even do not need to have a formal education to know or use them. One of the reasons can be that it is frequently use in daily life accounting. Other number systems are used in more specified fields such as computing and hence would need to be learned.

Octal Numbers

Octal numbers are not that commonly used as compared to other numbers and are mostly used in computing graphics, text and famous operating system such as UNIX also uses octal numbers for their file protection system. Octal numbers have total of 8 unique representations which can be combined together to make more octal number representations. Octal numbers are difficult to understand for a normal person who has limited number of understanding about the number system. As after 7 different numbers are used to represent numbers from 7 onwards and hence they seem physically bit difficult to comprehend. The number system needs to use a subscript of 8 with is number to represented they are not Denary but octal number otherwise confusion can easily occurred.

Hexadecimal Number System

Hexadecimal number are used where there are more options which needs to be represented off and are mostly commonly used in computing to represent different memory locations. Since binary, octal and hexadecimal have representations which are powers of 2 (power of 0 in binary, 3 in octal and 4 in hexadecimal) hence that makes them more suitable to different situations, which require different number representations. They are positively contributing to the daily life and to the technology and logical world as well and needs to be understood properly if one needs to take advantage of such technology.

Whilst the above gives uses of the binary, octal and hex number systems in different areas of IT and while some example are given the manager encourages you to research a wide range of examples for him to look at.

Binary Number System used in ASCII table and IP Address

Binary number system are also used in the ASCII table to represent different codes for different characters which then can be used into computing as well. ASCII number is more like a combination of binary numbers. Binary numbers are also used in IP addressing system again which is a combination of Binary number and are used in computing field. These IP addresses are of two different versions now one is known as IP 4 and other one is known as IP 6. These IP addresses are further sub divided into different classes such as class A, B and C where each class has a different number of hosts and network address.

The ASCII character set, each binary value between 0 and 127 is given a specific character. Most computers extend the ASCII characters set to use the full range of 256 characters available in a byte. The upper 128 characters handle special things like accented characters from common foreign languages.

In ASCII character set, each character is represented by 7 bits when stored in the computer and in an extended ASCII character set, each character is represented by 8 bits. Say for example:


0000000 represents NULL

Similar the word 'HELLO' if converted into binary using the ASCII to binary conversation could be represented as follows.

01001000 01000101 01001100 01001100 01001111(in decimal 72 69 76 79)

Please refer an ASCII character table for further understanding of this conversion.


Binary Conversation

Octal numbering system for file protection in UNIX

Every file or folder in UNIX has access permission. There are three types of permissions (what allowed to do with a file):

Read Access

Write Access

Execute Access

Permissions are defined for three types of users:

The owner of the file

The group that the owner belongs to

Other users

Thus, UNIX file permission are nine bits of information (3 types x 3 type of users), each of them may have just one of two values: allowed or denied.

Simply put, for each file it can be specified who can read or write from/to the file. For programs or scripts it also can be set if they are allowed to be executed.

Textual representation like "-rwxr-r-"

It is used in UNIX long directory listings. It consists of 10 characters. The first character shows the file type. Next 9 characters are permissions, consisting of three groups: owner, groups, others. Each group consists of three symbols: rwx (in this order), if some permission is denied, then a dash "-"is used instead. For example



Symbol in the position 0 ("-") is the type of the file. It is either "d" if the item is a directory or "l" if it is a link, or "-" if the item is a regular file.

Symbols in positions 1 to 3 ("rwx") are permissions for the owner of the file.

Symbols in positions 4 to 6 ("r--") are permissions for the group.

Symbols in positions 7 to 9 ("r--") are permissions for others.


Read access is allowed


Write access is allowed


Execute access is allowed


Replaces "r", "w" or "x" if according access type is denied

Numeric (octal) representation like "664"

If a numeric representation is used (like in chmod-command, for example), then it is in the octal format (with the base of 8), and digits involved are 0 to 7. Octal format is used for the simplicity of understanding: every octal digit combines read, write and execute permissions together. Respective access rights for owner group and others (in this order) are the last three digits of the numeric file permissions representation. Example: "0644". Here the second digit ("6" in the example) stands for rights of the owner, the third digit ("4" in the example) stands for rights of the group, the fourth digit ("4" in the example) stands for rights of others.

The below tales show what numeric values mean:

Octal digit

Text equivalent

Binary value





All types of access are denied




Execute access is allowed only




Write access is allowed only




Write and execute access are allowed




Read access is allowed only




Read and execute access are allowed




Read and write access are allowed




Everything is allowed

According to the above table we can see that "1" stands for execute only, "2" stands for write only, "4"stands for read only. To combine the permission you can simply add 1, 2 and 4 to get a needed combination. For instance, to get read and write permission, you add 4 (read) and 2 (write), thus getting 6 (read and write). To get read and execute permissions, you add 4 (read) and 1 (execute), this getting 5 (read and execute).


755 on a file would mean rwx r-x r-w permission on the file. Simply convert the octal number to the binary equivalent and enable the permission where the bits are 1.

755 would mean 111 101 101

In addition there is one more octet representing the Set user ID, set group ID, sticky bit which works in a similar way.

Octal digit

Binary value




setuid, setgid, sticky bits are cleared



sticky bit is set



setgid bit is set



setgid and sticky bits are set



setuid bit is set



setuid and sticky bits are set



setuid and setgid bits are set



setuid, setgid, sticky bits are set

Explain the use of binary in IP addressing for both V4 and V6?

Use of binary in IP addressing for V4:

Each IP in a V4 IP addressing consists of 32 bits. These 32 bits are divided into 4 octets of 8 bits each. An IP address is represented like this: A computer can understand only binary values and therefore each IP is stored in binary.

Each octet is represented as follows. For example if the value of the first octet is 128, it would be represented as follows:

















Therefore an IP would be stored as follows:

10000000 10000000 10000000 10000000

Use of binary in IP addressing for V6:

While IPv4 allows 32 bits for an Internet Protocol address, and can therefore support 232 (4,294,967,296) addresses, IPv6 uses 128-bit addresses, so the new address space supports 2128(3.4 x 1038) addresses.

This expansion allows for many more devices and user on the internet as well as extra flexibility in allocating addresses and efficiency for routing traffic.

The IPv6 128-bit address is divided along 16-bit boundaries. Each 16-but block is then converted to a 4-digit hexadecimal number, separated by colons. The resulting representation is called colon-hexadecimal. This is in contrast to the 32-bit IPv4 address represented in dotted-decimal format, divided along 8-bit boundaries, and then converted to its decimal equivalent, separated by periods.

The following example shows a 128-bit IPv6 address in binary form:



The following example shows this same address divided along 16-bit boundaries:

0010000111011010 0000000011010011 0000000000000000 00101111001110110000001010101010 0000000011111111 1111111000101000 1001110001011010

The following example shows each 16-bit block in the address converted to hexadecimal and delimited with colons.


IPv6 representation can be further simplified by removing the leading zeros within each 16-bit block. However, each block must have at least a single digit. The following example shows the address without the leading zeros:



Binary in describing class A, B and C IP addresses

The class of the address determines which part belongs to the network address and which part belongs to the node address. All nodes on a given network share the same network prefix but must have a unique host number.

Class A Network -- binary address start with 0, therefore the decimal number can be anywhere from 1 to 126. The first 8 bits (the first octet) identify the network and the remaining 24 bits indicate the host within the network. An example of a Class A IP address is, where "102" identifies the network and "168.212.226" identifies the host on that network.

Class B Network -- binary addresses start with 10, therefore the decimal number can be anywhere from 128 to 191. (The number 127 is reserved for loopback and is used for internal testing on the local machine.) The first 16 bits (the first two octets) identify the network and the remaining 16 bits indicate the host within the network. An example of a Class B IP address is where "168.212" identifies the network and "226.204" identifies the host on that network.

Class C Network -- binary addresses start with 110, therefore the decimal number can be anywhere from 192 to 223. The first 24 bits (the first three octets) identify the network and the remaining 8 bits indicate the host within the network. An example of a Class C IP address is where "200.168.212" identifies the network and "226" identifies the host on that network.

Hexadecimal for addressing memory

Memory addresses are displayed as two hex numbers. An example is C800:5. The part to the left of the colon (C800) is called the segment address, and the part to the right of the colon (5) is called the offset. The offset value can have as many as four hex digits. The actual memory address is calculated by adding a zero to the right of the segment address and adding the offset value, like this: C800:5 = C8000 + 5

= C8005

C8005 is called as the absolute or linear address of the memory.

Similarly F000:FFFD can be computed to get the following memory address.




FFFFD or 1,048,573(decimal)

The Segment: Offset addressing was introduced at a time when the largest register in a CPU was only 16-bits long which meant it could address only 65,536 bytes (64 KB) of memory, directly. But everyone was hungry for a way to run much larger programs! Rather than create a CPU with larger register sizes (as some CPU manufacturers had done), the designers at Intel decided to keep the 16-bit registers for their new 8086 CPU and added a different way to access more memory: They expanded the instruction set, so programs could tell the CPU to group two 16-bit registers together whenever they needed to refer to an Absolute memory location beyond 64 KB.

Classless Inter Domain Routing

Classless Inter Domain Routing. CIDR was invented several years ago to keep the internet from running out of IP addresses. The "classful" system of allocating IP addresses is very wasteful. Anyone who could reasonably show a need for more that 254 host addresses was given a Class B address block of 65533 host addresses. Even more wasteful were companies and organisations that were allocated Class A address blocks, which contain over 16 Million host addresses! Only a tiny percentage of the allocated Class A and Class B address space has ever been actually assigned to a host computer on the Internet.

CIDR specifies an IP address range using a combination of an IP address and its associated network mask. CIDR notation uses the following format -

where n is the number of (leftmost) '1' bits in the mask. For example,

applies the network mask to the 192.168 network, starting at This notation represents the address range - Compared to traditional class-based networking, represents an aggregation of the two Class C subnets and each having a subnet mask of In other words, = +

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