Binary = Computer Science 3.1 Data

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  • Binary numbering system
    • Binary
      • Binary Arithmetic
        • Binary shift
          • Moving the values to the left or right.
        • Arithmetic Shift
          • Each shift to the left doubles the number, each shift to the right performs integer division buy two.
        • Overflow
          • Occurs when the number you want to store is too big for the bits assigned to it. Happens when Arithmetic shift left shifts a one.
        • Logic Shift
          • Looks like arithmetic shift but the numeric value is unimportant, sign(+,-) is irrelevant and overflow is ignored.
      • Addition
        • 0 + 0 = 0
        • 0 + 1 = 1
        • 1 + 0 = 1
        • 1 + 1 = 10
        • 1 + 1 + 1 = 11
      • Hexadecimal
        • 0 = 0 = 0000
        • 1 = 1 = 0001
        • 2 = 2 = 0010
        • 3 = 3 = 0011
        • 4 = 4 = 0100
        • 5 = 5 = 0101
        • 6 = 6 = 0110
        • 7 = 7 = 0111
        • 8 = 8 = 1000
        • 9 = 9 = 1001
        • 10 = A = 1010
        • 11 = B = 1011
        • 12 = C = 1100
          • 13 = D = 1101
            • 14 = E = 1110
              • 15 = F = 1111
    • Unsigned integers
      • An integer is a whole number, and an unsigned integer is one that is not negative.
    • Sign and Magnitude
      • This is one system that can represent both positive and negative numbers.
      • It is not widely used as it contains values for 0's and minus 0's which can make coding complicated.
    • Two's Complement
      • This is a different numbering system which can represent both positive and negative numbers.

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