Data Types

• • Integer
  • Real
  • Boolean
  • Character
  • String
• • A primitive data type is a basic data type provided as a foundational building block
  • Complex data types are constructed on these
• Casting is when you convert one data type to another
• Eg: str(3) returns "3"
• We can represent negative numbers in binary

  This is done by using the most significant bit to represent sign

  if the MSB is 0 then the number is positive

  if the MSB is 1 then the number is negative
• During two's complement the Most Significant Bit is a negative number
• Eg: write -12 as a binary number using two's complement:

  The MSB is -128 so this is our number

  -12 fits into -128 so we have a 1 in our -128 column leaving 116

  64 fits into 116
• We can convert a positive binary number into its negative two's complement version:

  Eg: 12:

  12 in binary is 0 0 0 0 1 1 0 0

  Now, to convert, starting from the right, copy each number until the first 1. After that, swap each 0 for a 1 and 1 for 0:

  1 1 1 1 0 1 0 0
• During binary addition:

  0 + 0 = 0

  0 + 1 = 1

  1 + 1 = 0 carry 1

  1 + 1 + 1 = 1 carry 1
• All characters are either represented in ASCII or Unicode
• Each character has its own unique bit pattern
• A character set is the defined list of characters recognised by computer hardware and software with each character being represented by a unique bit pattenr
• ASCII stands for American Standard Code for Information Interchange
• ASCII is 7 bits

  It can store 128 characters
• Unicode was initially a 16 bit character set
• However, now Unicode is a 24 bit character set, so it provides us over 16 million different characters, making it more universal as it includes characters from different languages as well as emojis
• The main advantage of ASCII over Unicode is that it usually takes up much less space in memory than Unicode, despite representing less characters
• Hexadecimal is in base 16
• In hexadecimal:

  A - 10

  B - 11

  C - 12

  D - 13

  E - 14

  F - 15
• Computers do not use hexadecimal, but there is a close relationship between hexadecimal and a binary nibble, so they are useful for representing large binary numbers in a smaller number of digits, because they are just easier to read for humans.

  NOTE: They take up the same space in a computer though
• To convert denary to hexadecimal

  • convert denary number to binary
  • Then convert each nibble to hexadecimal
• We can also store fractional numbers in binary

  This is done by extending the number line to include negative powers of two. We place a binary point between 1 and 1/2

  
• The process used to store fractions is called fixed-point binary

  This however, limits the size of the number we can store, as bits are now being used to store the non-integer parts of the number
• We can increase the accuracy of storing numbers by changing the position of the binary point, by making it float up and down, meaning that more bits are either used for the integer, or the real part of the number
• We also need to store the position of the binary point

  This is done by splitting the number into two parts

  1. The mantissa : This is the number itself
  2. The exponent : The position of the binary point in the number
• We can shift binary numbers by moving all their bits to the left or to the right
• If we shift it to the left, we multiply it

  If we shift it to the right, we divide it
• the number of times you shift it tells you the number you are multiplying or dividing by
• When shifting, we knock off any bits that shift off from the left side

  We pad any blank spaces with a 0
• Eg: Shifting a binary number left 1 time multiplies it by 2, as 2^1 = 2

  Shitfing a binary number right 2 times divided it by 4, as 2^2 = 4
• A logical right shift will not work on negative numbers in two's complement will not work, as it turns the number positive
• In an arithmetic right shift, the vacant MSB in the new number is filled with the value of the previous MSB
• We can also apply masks to bit patterns

  Masking allows us to :

  • isolate and extract bit values in a sequence of bits
  • Toggle, and set bit values in a sequence of bits
  • They use the operators AND OR XOR
• Eg: use bitwise AND operation to apply a mask of 11110000 to the number 10011101

  1 0 0 1 1 1 0 1

  1 1 1 1 0 0 0 0

  1 and 1 = 1

  0 and 1 = 0

  0 and 1 = 0

  and so on
• Masks are used in routing traffic on a network

  Masks are used to isolate the networks and hosts in an IP address