3. fundamentals of data representation

• high-level programming languages can be understood by us as humans, whereas it will need to be translated into a more complex language for a computer to be able to execute it

  for example: Java, Python, etc
• low-level programming languages, also known as machine language, is understood by computers but not so much by humans

  this could simply be a line of binary or hexadecimal
• high level language must be translated to low level language before a computer is able to use it

  there are two methods of achieving this:

  • compilation translates the whole high-level code into low-level code using a compiler
  • interpretation translates the whole high-level code into smaller low-level instructions using an interpreter
• a complier:

  • uses the original code from the high-level programming language as the input to the compiler
  • the entire source code is compiled into low level machine language known as object code which is ready to be executed
• advantage and disadvantage to a complier

  • advantage - it is versatile and widely compatible
  • disadvantage - the whole original code must be re-translated if any changes are made which is inefficient for programmers
• an interpreter

  • translates a single high-level program into several low-level instructions
  • only translates each instruction when required, therefore no object code is generated
• advantage and disadvantage of an interpreter

  • advantage - when the source code is updated, only the effected instructions require re-translating
  • disadvantage - the process has to take place each time the program is executed which uses processing power and inefficient for the end users
• • denary is another term for a decimal number, which is any number from 0 to 9
  • this system is known as a base-10 system, simply due to using ten different digits
• • binary is a numerical system that computer systems use to perform instructions and communicate
  • each digit is just a single bit in size
  • binary is a type of system called a base-2 system
  • it uses two digits - those digits are 1 and 0
• we can use scientific notation to represent long sums in short

  • for example a*a*a*a*a*a can be converted into a value that uses scientific notation
  • the new value would become a^6
• • each time the number of binary digits increases, the possible outcomes double
  • when referring to these, we can use scientific notation
  • e.g. 2 bits forms 4 binary outcomes 2^2, 3 bits forms 8 binary outcomes 2^3
• • hexadecimal is a place-value system used by computer systems in many different ways
  • hexadecimal is also much easier to interpret by humans than binary
  • a single hexadecimal digit is a nibble in size, which is equal to four bits
  • hexadecimal is a base-16 system
• the values of hexadecimal:

  1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• converting decimal to binary:

  • we divide the decimal whole number by 2 continuously until we reach zero or 0.5
  • each time we divide by 2 we make a note of the answer - we write a 0 in the binary column
  • not all numbers will divide to equal a whole number - when this occurs we write a 1 in the binary column and continue
  • it is important to ignore the 0.5 and divide by the number without 0.5; so for example if the calculation is 7/2 = 3.5 we must ignore the .5 and divide 3 next
  • once the column is complete, we write the binary digits from BOTTOM to TOP which gives us our binary answer
• converting hexadecimal to binary

  • hexadecimal values go from 1 to F
  • convert each hexadecimal value to denary and then from denary to binary
  • for example, A in hex is 10 in denary, and 10 in binary is 1010
  • this process continues until the complete hexadecimal figure has been converted
• convert the decimal number 228 to binary

  11100100
• convert the decimal number 251 to binary

  11111011
• convert the hexadecimal number D2 to binary

  11010010
• convert the hexadecimal number 7AB8 to binary(first bit done for you)

  (0)111101010111000
• bits and bytes

  A) bit

  B) b

  C) nibble

  D) kilobit

  E) Kb

  F) megabit

  G) Mb

  H) gigabit

  I) Gb

  J) terabit

  K) Tb

  L) 4

  M) 1000

  N) 1000

  O) 1000

  P) 1000

  Q) lower

  R) byte

  S) B

  T) kilobyte

  U) KB

  V) megabytes

  W) MB

  X) gigabytes

  Y) GB

  Z) terabytes

  [) TB

  \) 1024

  ]) 1024

  ^) 1024

  _) 1024

  `) upper

  
• there are 8 bits in a byte
• calculating the data rate

  data rate = file size / time taken for transfer (s)
• convert 3,450 megabytes into bytes

  3.618 x 10 ^ 9
• standard ASCII stores up to 128 characters at just 7 bits per character