Data Representation//Ethical+Legal+Environmental

• Task 2: Place the following numbers into their correct columns and then write them as a binary number by combining them together and finally work out the decimal total by adding together the column headings which contain a 1


  1. 1 x 8, 0 x 4, 1 x 2 and 1 x 1

  2. 1 x 8, 1 x 4, 0 x 2 and 0 x 1

  3. 1 x 2 and 1 x 1
• Computers use binary to store data. A binary digit, more commonly known as a bit, is the smallest piece of data possible in a computer system, it is either a 1 or a 0.
• The circuits in a computer's processor are made up of billions of transistors. A transistor is a microscopic device that open and close circuits to allow electrical signals to either flow or not flow through the circuit. The digits 1 and 0 used in binary reflect the on and off states of a transistor.

  
• Computer programs, as you know them, are known as a "high-level language" and although may be full of technical jargon are more human-friendly than the language used by computers. The high-level languages must be converted into machine code which are binary commands to tell the computer what to do, where to store the data and where they are in the program.
• All software, programs, images, music, documents, video and any other information that is processed by a computer is stored using these on/off electrical pulses in the computer and can be represented in binary.
• Hexadecimal (base 16)


  A number system that uses 16 digits (0-9 and A-F)
• Hexadecimal numbers are used as a shorthand notation for long binary numbers, shortening them considerably and reducing the likelihood of errors.
• One hexadecimal digit can represent 4 binary digits, making converting between binary and hexadecimal easier than other number bases.
• Decimal to binary conversion steps


  • Decide on the column to start with (lower than or equal to the value)
  • Find the remainder
  • Repeat steps 1 and 2 until no more remainder
  • Fill in other columns with 0s
• Binary to hexadecimal conversion steps


  • Split the binary number into blocks of 4 bits starting from the right
  • Convert each block of 4 bits into a hexadecimal digit
• Hexadecimal to binary conversion steps


  • Convert each hexadecimal digit into a decimal number
  • Convert each decimal number into binary
  • Combine the binary numbers
• To convert hexadecimal to decimal, first convert the hexadecimal to binary, then convert the binary to decimal.
• Number base notation uses a subscript to indicate the number base, e.g. 1002 is binary for 4, 10010 is decimal for 18.
• Convert decimal to binary


  1. Convert decimal number to binary

  2. Convert binary to hexadecimal
• Convert hexadecimal to decimal


  1. Convert hexadecimal to binary

  2. Convert binary to decimal
• A bit is the fundamental unit of information and a byte is a group of 8 bits
• Units of information


  • Bit (b)
  • Byte (B)
  • Kilobytes (kB)
  • Megabytes (MB)
  • Gigabytes (GB)
  • Terabytes (TB)
  • Petabytes (PB)
  • Exabyte (EB)
  • Zettabyte (ZB)
  • Yottabyte (YB)
• Data storage requirements


  • A typical line of text from a book (90 bytes)
  • One page of text from a standard novel (4 kB)
  • MP3 song (3.5 MB)
  • A Blu-ray movie (22 GB)
• Binary addition


  1. Add the first column

  2. Add the next column, including any carry over

  3. Continue adding columns, including any carry over

  4. Move any final carry over to the main answer row
• Shifting binary digits to the right


  Divides the number by 2
• Shifting binary digits to the left

  Multiplies the number by 2
• 1. bit ASCII


  Character encoding method where each character is represented by 7 binary bits

  
• Unicode


  Character encoding method that can represent characters from most of the world's writing systems
• T


  111 0100
• t


  011 0101
• 5


  101 0101
• U


  111 0101
• u


  011 0110
• 6


  101 0110
• V


  111 0110
• v


  011 0111
• 7


  101 0111
• W


  111 0111
• w


  011 1000
• 8


  101 1000
• X


  111 1000
• x


  011 1001
• 9


  101 1001
• Y


  111 1001
• y


  011 1010