CSCI 1120 Lecture Notes - Lecture 3: Radix Point, English Alphabet, Floating Point
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12 Sep 2018
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The mantissa is the actual precision point of the fraction. Assume that the radix point is always a 1, as it will always be true. If it was a 0, it would not exist. When all eight bits in the exponent are set to 0, the floating-point value is set to 0, because no values are true. When all eight bits in the exponent are set to 1, the floating-point value is set to infinity, because all values are true. Every time we use pi, we are going to make a small numerical error, so we need to find the value closest to 0 that we can encode using 32 bits, which we can find through trial and error. The smallest value we can get is 00000000100000000000000000000000, and this is 2-126 . No value smaller than this is possible, as if anything is smaller the system will round this up or down and be inaccurate.