Data representation, types and structures

Logical Operators
1. Truth Tables
  1. AND
    1. Either they are both are on, otherwise it is off
  2. NOT
    1. It will be the inverse to itself if it isn't
  3. OR
    1. One or the other is on, not mattering if it is both on
  4. XOR
    1. One or the other is on, however if both are one then it equals off
2. Shifts
  1. Logical
    1. One bit 'falls off' (possibly into the Carry flag), and a 0 is shifted in.
  2. Arithmetic
    1. Similar to a Logical shift, but the sign bit remains unchanged.
    2. To the left is multiplying by 2
    3. To the right is dividing by 2
3. Encryption
  1. Uses the XOR commamd
  2. X + Key = Encryption
    1. Encryption + Key = X
Hexadecimal
1. A shorthand method for representing binary numbers.
  1. More convenient alternative coding method.
    1. Used because they are more readily converted to or from binary.
2. The hexadecimal number system has a base of 16, and uses the following symbols:
3. Converting
  1. To Decimal
    1. Give place values of 16 to the power of the place of the hexadecimal from left to right starting from 0
      1. Multiply the 16 value with the number place in the hexadecimal table
        Adding them together will give you the decimal value
  2. From Decimal
    1. Divide the decimal by 16
      1. Get the answer in whole number/remainder form
        Convert the first number into hexadecimal via its place on the table then the remainder
  3. To Binary
    1. Find each character from the hexadecimal, convert it to its number place
      1. Convert the number place into binary and put back together
  4. From Binary
    1. Convert the binary into a decimal
      1. Change the decimal into hex, dependant on its place in the table
Two's Compliment and S&M
1. Sign And Magnitude
  1. The binary is split into 2 pieces, the sign and the magnitude
    1. The first digit (Normally 128) is the sign, and if it is 0 then it is positive and if it is 1 then it is negative
      1. +95 = 01011111
      2. -95 = 11011111
  2. Restricted to 8 bit words and only between -127 and 127
2. Two's Compliment
  1. The amount of bits that can be stored depends on the word size
  2. Characteristics
    1. Allows a number to be shown as a negative
    2. Makes subtraction easy by replacing addition
    3. Efficient in the process of adding
    4. Requires no separate provision for inclusion of the sign
    5. The values are stored precisley
  3. Subtraction
    1. Subtraction in two’s complement is performed by negating the 2nd number and adding it to the 1st
      1. To negate a number change all 0s to 1s and all 1s to 0s, then add 1. This is complementation
  4. Integer Addition
    1. 0 + 0 (no carry) = 0
    2. 0 + 0 (carry) = 1
    3. 0 + 1 (no carry) = 1
    4. 0 + 1 (carry) = 0
    5. 1 + 1 (no carry) = 0
    6. 1 + 1 (carry) = 1 (carry)

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Data representation, types and structures

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