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Intro (Information Representation (Other systems (Counting in base 3 (0 1…

- - - - This is the carry system
        
        0
        1
        2
        3
        4
        5
        6
        7
        8
        9
        10
        
        Instead of making 10 a new symbol we just reuse 1 and 0
        
        What we're really doing
        
        28
        +
        24
        =
        52
        
        19
        +
        19
        =
        38
        
        When adding one column to another gets you a number over 9 we make that column the first digit then add 1 to the next column
  - - - 0
        1
        2
        10
        11
        12
        20
        ...
    - - 0
        1
        10
        11
        100
        101
        110
        111
        1000
        ...
  - - - Every digit is in base 2
        
        1 0 1 1 0
        \(1*2^4+0*2^3+1*2^2+1*2^1+0*2^0=22\)
    - - Read from bottom to top so 22 in decimal is 10110 in binary
  - - - V=1 means overflow
        V=0 means not
        
        How can we tell if there's an overflow?
        
        Convert the numbers into decimal and add them. If their sum is outside range written as decimal then it's overflow
        
        0 1 0 1 1 0
        +
        0 0 1 1 0 0
        =
        1 0 0 0 1 0
        
        Two Rules
        
        If the sum of two numbers with the sign bits off yields a result number with the sign bit on, the "overflow" flag is turned on.
        
        If the sum of two numbers with the sign bits on yields a result number with the sign bit off, the "overflow" flag is turned on
    - - 0 1 0 1 1 0
        +
        0 0 1 1 0 0
        =
        1 0 0 0 1 0
        
        Both numbers have bit off but adding them caused it to be on
        Overflow
        
        No Overflow
        0 0 0 0 1 1
        +
        0 1 0 1 0 1
        =
        0 1 1 0 0 0
        
        1 0 0 1 1 0
        +
        1 0 0 0 1 0
        =
        0 0 1 0 0 0
        
        Overflow
        Both started with sign bit turned on but result has sign bit turned off
- - - - To do that we need to know the one's complement. This is just switching 1s with 0s and 0s with 1s
        
        C is the carry
        If C=0 then nothing is carried
        If C=1 then there is a 1 carried
        
        5 in binary is
        0 0 0 1 0 1
        
        so -5 in binary is
        NOT 0 0 0 1 0 1= 1 1 1 0 1 0
        1 1 1 0 1 0
        +
        0 0 0 0 0 1
        =
        1 1 1 0 1 1
        
        Adding 5 and -5 we get 0
        
        0 0 0 1 0 1
        +
        1 1 1 0 1 0
        =
        C=0 \(\quad\) 1 1 1 1 1 1
        
        1 1 1 1 1 1
        +
        0 0 0 0 0 1
        =
        C=1 \(\quad\) 0 0 0 0 0 0
        
        1 more item...
    - - NEG x=!+NOT x
      - NOT is just switching 1s with 0s and 0s with 1s
    - - A negative number must have a 1 in the leftmost number
        
        You can tell if a number is even or odd by the rightmost column
        0 = even
        1 = odd
        
        -7 is really -6 + 1
        
        -6=1+ NOT 6
        6 = 0 1 1 0
        NOT 6 = 1 0 0 1
        
        1 0 0 1
        +
        0 0 0 1
        =
        1 0 1 0
        
        1 0 1 0
        +
        0 0 0 1
        =
        1 0 1 1
        
        -7= 1 0 1 1 in binary
        
        DOESN'T mean every number with a 1 in the leftmost column is a negative number
  - - - Same as leftmost column
    - - Same as rightmost column