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.

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• 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:

 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:

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:

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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