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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.

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.

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