Data representation, types and structures

Data representation, types and structures

1. Logical Operators

   • Truth Tables
     • AND
       • Either they are both are on, otherwise it is off
     • NOT
       • It will be the inverse to itself if it isn't
     • OR
       • One or the other is on, not mattering if it is both on
     • XOR
       • One or the other is on, however if both are one then it equals off
   • Shifts
     • Logical
       • One bit 'falls off' (possibly into the Carry flag), and a 0 is shifted in.
     • Arithmetic
       • Similar to a Logical shift, but the sign bit remains unchanged.
       • To the left is multiplying by 2
       • To the right is dividing by 2
   • Encryption
     • Uses the XOR commamd
     • X + Key = Encryption
       • Encryption + Key = X

2. Hexadecimal

   • A shorthand method for representing binary numbers.
     • More convenient alternative coding method.
       • Used because they are more readily converted to or from binary.
   • The hexadecimal number system has a base of 16, and uses the following symbols:
   • Converting
     • To Decimal
       • Give place values of 16 to the power of the place of the hexadecimal from left to right starting from 0
         • Multiply the 16 value with the number place in the hexadecimal table
           • Adding them together will give you the decimal value
     • From Decimal
       • Divide the decimal by 16
         • Get the answer in whole number/remainder form
           • Convert the first number into hexadecimal via its place on the table then the remainder
     • To Binary
       • Find each character from the hexadecimal, convert it to its number place
         • Convert the number place into binary and put back together
     • From Binary
       • Convert the binary into a decimal
         • Change the decimal into hex, dependant on its place in the table

3. Two's Compliment and S&M

   • Sign And Magnitude
     • The binary is split into 2 pieces, the sign and the magnitude
       • 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
         • +95 = 01011111
         • -95 = 11011111
     • Restricted to 8 bit words and only between -127 and 127
   • Two's Compliment
     • The amount of bits that can be stored depends on the word size
     • Characteristics
       • Allows a number to be shown as a negative
       • Makes subtraction easy by replacing addition
       • Efficient in the process of adding
       • Requires no separate provision for inclusion of the sign
       • The values are stored precisley
     • Subtraction
       • Subtraction in two’s complement is performed by negating the 2nd number and adding it to the 1st
         • To negate a number change all 0s to 1s and all 1s to 0s, then add 1. This is complementation
     • Integer Addition
       • 0 + 0 (no carry) = 0
       • 0 + 0 (carry) = 1
       • 0 + 1 (no carry) = 1
       • 0 + 1 (carry) = 0
       • 1 + 1 (no carry) = 0
       • 1 + 1 (carry) = 1 (carry)

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