By Oded Goldreich
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75 – – – – • • • • • • • • • • • – – – – • • • • • • • • • • • • • • • • • • • ––– • • • • • • • • • • • • • • • • • • • •––– • • • • • • • • • • • • • • • • • • • • • • ––– • • • • • • • • • • • • • • • • • • • • • •––– • • • • • • • • • • • • • • • • • • •–– • • • • • • • • • • • • • • • • • •–– • • • • • • • • • • • • • • • • • • • • –– • • • • • • • • • • • • • • • • • • • –– • • • • • • • • • • • – • • • • • • +++ – • • • • • • • • +++ +++++++ – +++++++++++ – +++++++ +++++++++++ ????????????????????????????????
Just as the sign bit positive (blank) or – is written to the left of the leftmost digit as a two-state indicator of the sign, exactness is a two-state indicator where the bit indicating exact (blank) or ∫ is written just to the right of the rightmost digit. When we want to be more clear, we explicitly put a “+” in front of a positive number instead of a blank. ” Or put another way, all the bits after the last one shown are 0. It only takes one bit to store the sign of a number, and it only takes one bit, the ubit, to store whether it does or does not have more bits than the format is able to store.
7 6 5 4 3 2 1 1 0 11 1 11 0 10 1 10 0 01 1 01 0 00 00 0 Bit String We can show the value represented by bit strings with a value plot. In a value plot, the horizontal axis shows the bit strings, sorted in numerical order as binary integers. The vertical axis shows the value expressed by the string, shown in decimal form, for a particular format. Since the bit strings represent specific numbers, the plot is a series of discrete points, not a continuous line or curve. Some people prefer to understand concepts via pictures, others prefer symbolic formulas, and still others like to see actual numbers.