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The Binary System

Binary System: A system of ones(1) and zeroes(0) which is the building block in a computer.
- Computers have millions of tiny switches which can either be in an ON or OFF position.
- 1 represents ON and 0 represents OFF position of a switch.
- Different combinations of these 1s and 0s hold different meanings to a computer.
Binary is a number system based on the number 2, i.e it counts in multiples of 2. Like 2,4,8,16 and so on.
Example use of Binary:
- If the register contains 1 0 1 0 1 0 1 0 this means ‘motor B is ON and motor C is ON and both motors are turning to produce FORWARDS motion’. Effectively, the vacuum cleaner is moving forwards.

Conversions Between Binary And Denary

Denary: A number system with a base of 10.
While converting a Binary value to Denary, always begin from the right hand side.
- Substitute the values with powers of 2 , starting from 2^0
- Add all the values in places of 1s only for the denary value. Using 00101101 as an example:

0	0	1	0	1	1	0	1
2^7 = 128	2^6 = 64	2^5 = 32	2^4 = 16	2^3 = 8	2^2 = 4	2^1 = 2	2^0 = 1

 32 + 8 + 4 + 1 = 45

In order to convert a Denary number to a Binary value, repetitive division is used. Using 107 as an example:

Measurement Of The Size Of Computer Memories

Bit: One Binary digit.
Byte: 8 Bits make up a Byte.
- Some computers also use larger Bytes but their Bits are always in multiples of 8.
Different memory sizes:

Name Of Memory Size	Number Of Bits	Number Of Bytes
1 Kilobyte (KB)	2^10	1024
1 Megabyte (MB)	2^20	1024^2
1 Gigabyte (GB)	2^30	1024^3
1 Terabyte (TB)	2^40	1024^4
1 Petabyte (PB)	2^50	1024^5

The Hexadecimal System

Hexadecimal System: A number system with base 16, thus every digit is represented by 16 values. Its also called ‘Hex’.
The table for equal values of Binary, Denary and Hex:

Binary	Denary	Hexadecimal
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
011q	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F

Conversions Between Binary And Hexadecimal

Converting from Binary to Hexadecimal is a fairly easy process.
Starting from the right and moving left, split the binary number into groups of 4 bits. If the last group has less than 4 bits, then simply fill in with 0s from the left.
Take each group of 4 bits and convert it into the equivalent hexadecimal digit using the table.
To convert from Hex to Binary, simply look at the corresponding values in the table.

Conversions Between Hexadecimal And Denary

To convert from Hex to Denary, use the same method as when converting from Binary to Denary, except using the powers of 16 instead of 2 this time. Add the total to get the Denary value.
In conversion from Denary to Hex, yet again a familiar method is used.
- Repeatedly divide the number by 16.
- Read the remainders from the bottom.
- Replace two digit numbers with Hex values.

Uses Of Hexadecimal System

Memory Dumps: The contents from the computer memory which are being sent to a printer or monitor etc.
- Hex is used as it takes lesser space than Binary and is easier to use.
- It is also used to trace errors in softwares and programs.
- It can represent the location of contents in computer memory.
Hyper Text Markup Language (HTML): A markup language used in developing web pages.
- Hex values are used to store colours of text.
Media Access Control (MAC): A unique address given to a device to identify it on the Internet.
- It refers to the Network Interface Card (NIC) of the device.
- Made of 48 Bits shown as 6 groups of Hex Digits.
- Form: NN – NN – NN – DD – DD – DD or NN:NN:NN:DD:DD:DD
- The first half is identity number of manufacturer and second half is serial number of the device.
- Two types of MAC addresses, Universally Administered MAC Address (UAA) and Locally Administered MAC Address (LAA).
- UAA: Common and set by the manufacturer at the factory. Very rarely changed.
- LAA: Set by an organisation when a change of MAC address may be needed. The possible reasons for this might be:
  - Certain software used on mainframe systems needing all the MAC addresses of devices to fall into a strict format.
  - To bypass a MAC address filter on a router or a firewall for security reasons.
  - To get past certain types of network restrictions.
Web Addresses:
- ASCII Code: A code written in Hex and given to each character on a keyboard.
  - Used in representing web addresses in URLs.
Assembly and Machine Code: True codes are written in Binary but as it is more error prone, time consuming and complicated, Hexadecimal is used by programmers.

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CH 01 : Binary Systems And Hexadecimal

The Binary System

Binary System: A system of ones(1) and zeroes(0) which is the building block in a computer.
- Computers have millions of tiny switches which can either be in an ON or OFF position.
- 1 represents ON and 0 represents OFF position of a switch.
- Different combinations of these 1s and 0s hold different meanings to a computer.
Binary is a number system based on the number 2, i.e it counts in multiples of 2. Like 2,4,8,16 and so on.
Example use of Binary:
- If the register contains 1 0 1 0 1 0 1 0 this means ‘motor B is ON and motor C is ON and both motors are turning to produce FORWARDS motion’. Effectively, the vacuum cleaner is moving forwards.

Conversions Between Binary And Denary

Denary: A number system with a base of 10.
While converting a Binary value to Denary, always begin from the right hand side.
- Substitute the values with powers of 2 , starting from 2^0
- Add all the values in places of 1s only for the denary value. Using 00101101 as an example:

0	0	1	0	1	1	0	1
2^7 = 128	2^6 = 64	2^5 = 32	2^4 = 16	2^3 = 8	2^2 = 4	2^1 = 2	2^0 = 1

 32 + 8 + 4 + 1 = 45

In order to convert a Denary number to a Binary value, repetitive division is used. Using 107 as an example:

Measurement Of The Size Of Computer Memories

Bit: One Binary digit.
Byte: 8 Bits make up a Byte.
- Some computers also use larger Bytes but their Bits are always in multiples of 8.
Different memory sizes:

Name Of Memory Size	Number Of Bits	Number Of Bytes
1 Kilobyte (KB)	2^10	1024
1 Megabyte (MB)	2^20	1024^2
1 Gigabyte (GB)	2^30	1024^3
1 Terabyte (TB)	2^40	1024^4
1 Petabyte (PB)	2^50	1024^5

The Hexadecimal System

Hexadecimal System: A number system with base 16, thus every digit is represented by 16 values. Its also called ‘Hex’.
The table for equal values of Binary, Denary and Hex:

Binary	Denary	Hexadecimal
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
011q	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F

Conversions Between Binary And Hexadecimal

Converting from Binary to Hexadecimal is a fairly easy process.
Starting from the right and moving left, split the binary number into groups of 4 bits. If the last group has less than 4 bits, then simply fill in with 0s from the left.
Take each group of 4 bits and convert it into the equivalent hexadecimal digit using the table.
To convert from Hex to Binary, simply look at the corresponding values in the table.

Conversions Between Hexadecimal And Denary

To convert from Hex to Denary, use the same method as when converting from Binary to Denary, except using the powers of 16 instead of 2 this time. Add the total to get the Denary value.
In conversion from Denary to Hex, yet again a familiar method is used.
- Repeatedly divide the number by 16.
- Read the remainders from the bottom.
- Replace two digit numbers with Hex values.

Uses Of Hexadecimal System

Memory Dumps: The contents from the computer memory which are being sent to a printer or monitor etc.
- Hex is used as it takes lesser space than Binary and is easier to use.
- It is also used to trace errors in softwares and programs.
- It can represent the location of contents in computer memory.
Hyper Text Markup Language (HTML): A markup language used in developing web pages.
- Hex values are used to store colours of text.
Media Access Control (MAC): A unique address given to a device to identify it on the Internet.
- It refers to the Network Interface Card (NIC) of the device.
- Made of 48 Bits shown as 6 groups of Hex Digits.
- Form: NN – NN – NN – DD – DD – DD or NN:NN:NN:DD:DD:DD
- The first half is identity number of manufacturer and second half is serial number of the device.
- Two types of MAC addresses, Universally Administered MAC Address (UAA) and Locally Administered MAC Address (LAA).
- UAA: Common and set by the manufacturer at the factory. Very rarely changed.
- LAA: Set by an organisation when a change of MAC address may be needed. The possible reasons for this might be:
  - Certain software used on mainframe systems needing all the MAC addresses of devices to fall into a strict format.
  - To bypass a MAC address filter on a router or a firewall for security reasons.
  - To get past certain types of network restrictions.
Web Addresses:
- ASCII Code: A code written in Hex and given to each character on a keyboard.
  - Used in representing web addresses in URLs.
Assembly and Machine Code: True codes are written in Binary but as it is more error prone, time consuming and complicated, Hexadecimal is used by programmers.