DATA REPRESENTATION

• Number systems


  • Natural numbers
  • Integer numbers
  • Rational numbers
  • Irrational numbers
  • Real numbers
• Natural numbers


  All positive numbers and zero
• Integer numbers


  All whole numbers and zero
• Rational numbers


  Numbers that can be written exactly as a fraction of one number over another, includes zero
• Irrational numbers


  Numbers that cannot be written exactly as a fraction, e.g. pi
• Real numbers


  All possible real world quantities, includes all irrational and rational numbers
• Ordinal numbers


  Integers that describe the numerical positions of objects in relation to others, e.g. 1st, 2nd, 3rd
• Counting how many objects you have

  Uses natural numbers
• Measuring a quantity

  Uses real numbers
• Decimal


  Base 10, 0-9
• Binary


  Base 2, 0-1
• Hexadecimal


  Base 16, 0-9 then a-f
• Hexadecimal


  • Most compact, can represent the same number as binary or decimal using less digits
  • Useful as a shorthand representation of binary because easy to convert between them
• Bit


  Fundamental unit of information that only takes 2 values - 1 and 0
• Byte


  8 bits
• Nybble


  4 bits
• 2^n values that can be represented with n bits
• Unsigned binary


  Can represent a range of decimal numbers from 0 to (2^n)-1 if n is the number of bits
• Twos complement


  Can represent a range of numbers from (2^n-1)-1 to -2(^n-1) if n is the number of bits
• Absolute error


  The actual amount by which a value is inaccurate, calculated by finding the difference between the given value and actual value
• Relative error


  Measure of uncertainty in a given value compared to the actual value, relative to the size of the given value. Calculated as absolute error / actual value
• Floating point


  Allows greater range of numbers with given number of bits because exponent can be positive or negative, so large exponent small mantissa allows large range but little precision, whilst small exponent and large mantissa allow for good precision but small range
• Fixed point


  Placement of fixed binary point determines precision - close to left gives good precision but small range, range increases precision decreases the further you move right
• Floating point numbers normalised to provide maximum precision, involves ensuring number starts with 01 for positive or 10 for negative
• Binary underflow


  When very small numbers cannot be represented with the number of bits
• Binary overflow


  When a number is too large to be represented with the available bits
• Information coding system


  Matches characters to character codes when computers need to represent a character
• Character code


  A decimal digit used to represent a character
• ASCII


  Uses 7 bits to represent A-Z, 0-9 and symbols, only represents latin alphabet
• Unicode


  Uses anywhere from 8 to 48 bits to represent much wider range of characters than ASCII
• Parity bit


  A single bit added to a transmission used to check for errors in data, value is calculated based on the data itself
• Even parity


  Value of parity bit chosen to make the total number of 1s in the data even
• Odd parity


  Value of parity bit chosen to make the total number of 1s in the data odd
• Parity check


  Confirming that the value of the received parity bit conforms to the type of parity (even or odd) in use - if incorrect, computer requests retransmission of the data
• Majority voting


  Each bit of data is transmitted multiple times and when received, the most commonly occurring value is taken to be correct
• Majority voting


  • Doesn't just detect but also corrects the error so no need for retransmission
  • Can correct errors when values of multiple bits have changed which parity bits can't do
• Majority voting

  • Disadvantage: volume of data being transmitted is increased so time taken increases
• Checksums


  Similar to parity bits, involve adding a value determined by the data itself to the data. Algorithm used to determine value of checksum based on data. No agreed algorithm. Once received, recipient can remove checksum and apply same algorithm to check it matches - if not, cannot correct itself so must retransmit data
• Check digit


  Type of checksum where only a single digit is added to the data, reducing the number of different algorithms that could be used and so the variety of errors that the method can detect
• Analogue data


  Continuous, no limits to the values the data can take